Please refer to Conic Sections MCQ Questions Class 11 Mathematics below. These MCQ questions for Class 11 Mathematics with answers have been designed as per the latest NCERT, CBSE books, and syllabus issued for the current academic year. These objective questions for Conic Sections will help you to prepare for the exams and get more marks.

**Conic Sections MCQ Questions Class 11 Mathematics**

Please see solved MCQ Questions for Conic Sections in Class 11 Mathematics. All questions and answers have been prepared by expert faculty of standard 11 based on the latest examination guidelines.

**MCQ Questions Class 11 Mathematics Conic Sections**

**Question. Let P be a variable point on the ellipse x2/25 + y2/16 = 1with foci at S and S¢. If A be the area of DPSS¢, then the maximum value of A is**

(a) 24 sq units

(b) 12 sq units

(c) 36 sq units

(d) None of these

## Answer

B

**Question: A line meets the coordinate axes in A B and .A circle is circumscribed about the ∆OAB. The distances from the points A and Bof the side AB to the tangent at O are equal to m n and respectively. Then, the diameter of the circle is**

(a) m (m+ n)

(b) n (m+n)

(c) m- n

d) None of these

## Answer

D

**Question: Let L _{1} be a straight line passing through the origin and L_{2} be the straight line x+ y = 1. If the intercepts made by the circle x2+y^{2-}x+3y=0 on L_{1} and L_{2 }are equal, then L_{1} can be represented by**

(a) x+ y = 0

(b) x- y = 0

(c) 7x+y=0

(d) x- 7y=0

## Answer

B

**Question: Consider the following statements****I. Circle x ^{2}+y^{2}-x-y-1=0 is completely inside the circle x^{2}+y^{2}– x+2y-7=0. **

**II. Number of common tangents of the circles x**

^{2}+y^{2}+14x+12y+21=0 and x^{2}+y^{2}+2x-4y-4=0 is 4.**Which of these is/are correct?**

(a) Only I

(b) Only II

(c) Both I and II

(d) None of these

## Answer

A

**Question: The range of values of a such that the angle θ between the pair of tangents drawn from( a,0 ) to the circle x ^{2}+y^{2}=1 satisfies π/2<θ π,is**

(a) (1, 2)

(b) ( 1,√2)

(c) ( -√2,-1 )

(d) (-√2-1) ∪ (1,√2)

## Answer

D

**Question: Points (– 6, 0), (0, 6) and (–7, 7) are the vertices of ∆ABC. The incircle of the triangle has the equation**

(a) x^{2}+ y^{2} -9x -9y + 36 =0

(b) x^{2}+ y^{2 }+9x -9y + 36 =0

(c) x^{2}+ y^{2 }+9x +9y – 36 =0

(d) x^{2}+ y^{2 }+18x -18y +36 =0

## Answer

B

**Question: Two rods of lengths a b and slide along the x-axis and y-axis respectively in such a manner that their ends are concyclic. The locus of the centre of the circle passing through the end points is**

(a) 4(x^{2}+y^{2}) =a^{2 }+b^{2}

(b) x^{2}+y2 =a^{2} +b^{2}

(c) 4(x^{2}-y^{2}) =a^{2} -b2

(d) x^{2}-y^{2} =a^{2} -b^{2}

## Answer

C

**Question: The equations of the sides AB, BC and CA of a ∆ ABC are x +y = 1, 4x -y + 4 = 0 and 2x+ 3y= 6.****Circles are drawn on AB BC , and CA as diameters. The point of concurrence of the common chord is**

(a) centroid of the triangle

(b) orthocentre

(c) circumcentre

(d) incentre

## Answer

B

**Question: The set of values of c so that the equations y= |x|+c and x2+y2-8|x| -9 =0 have no solution, is**

(a) (- ∞, -3) ∪ (3,∞)

(b) ( -3,3), )

(c) (- ∞,5√2) ∪ (5√2,∞ )

(d) (5,√2-4, ∞)

## Answer

D

**Question: Two points P Q and are taken on the line joining the points A( 0,0) and B ( ,3a,0) such that AP= PQ=QB.****Circles are drawn on AP, PQ, QB and as diameters.****The locus of the points, the sum of the squares of the tangents from which to the three circles is equal to b ^{2} , is**

(a) x

^{2}+y

^{2}-3ax+2a

^{2}-b

^{2}=0

(b) 3(x

^{2}+y

^{2})-9ax+8a

^{2-}b

^{2}=0

(c) x

^{2}+y

^{2}-5ax+6a

^{2}-b

^{2}=0

(d) x

^{2}+y

^{2}-ax-b

^{2}=0

## Answer

B

**Question: If OA OB and are equal perpendicular chord of the circles x ^{2}+ y^{2}-2x + 4y= 0, then equations of OA and**

**OB are (where, O is origin)**

(a) 3x + y =0 and 3x-y =0

(b) 3x + y =0 and 3x-x =0

(c) x + 3y =0 and y-3x =0

(d) x + y = 0 and x-y= 0

## Answer

B

**Question: Equation of chord of the circle x ^{2}+y^{2}-3x-4y-4=0, which passes through the origin such that the origin divides it in the ratio 4 1: ,is**

(a) x = 0

(b) 24x+y=0

(c) 7x+24=0

(d) 7x-24y=0

## Answer

B

**Question: An isosceles right angled triangle is inscribed in the circle x ^{2}+y^{2}= r^{2}. If the coordinates of an end of the hypotenuse are ( a ,b), the coordinates of the vertex are**

(a) (-a,-b)

(b) (b,- a)

(c) (b, a)

(d) (-b,- a)

## Answer

B

**Question: In a ∆ABC, right angled at A, on the leg AC as diameter, a semi-circle is described. If a chord joins A with the point of intersection D of the hypotenuse and the semi-circle, then the length of AC equal to**

(a) ABx AD/√AB^{2}+ AD^{2}

(b) ABx AD/AB+ AD

(c) √ABx AD

(d) AB xAD/√AB^{2}-AD^{2 }

## Answer

D

**Question: A rhombus is inscribed in the region common to the two circles x ^{2}+y^{2}-4x-12=0 and x^{2}+y^{2}+4x -12=0 with two of its vertices on the line joining the centres of the circles. The area of the**

**rhombus is**

(a) 8 √3 sq units

(b) 4 √3 sq units

(c) 6 √3 sq units

(d) None of these

## Answer

A

**Question: A straight line with slope 2 and y-intercept 5 touches the circle, x ^{2}+y^{2}+16x+12y+c=0 at a point Q.Then, the coordinates of Q are**

(a) (-6,11)

(b) (-9,-13)

(c) ( -10,10-15)

(d) (-6,-7)

## Answer

D

**Question: Two circles with radii a b and touch each other externally such that θ is the angle between the direct common tangents (a >b ≥2) , then**

## Answer

D

**Question: A pair of tangents are drawn to a unit circle with centre at the origin and these tangents intersect at A enclosing an angle of 60°. The area enclosed by these tangents and the arc of the circle is**

(a) 2/√3 −π/6

(b) √3 -π/3

(c) π/3- √3/6

(d) √3 (1- π/6)

## Answer

B

**Question: The equation of a line inclined at an angle π/4 to the x-axis, such that the two circles x ^{2}+y^{2}=4, x^{2}+y^{2}-10x-14y+65=0 intercept equal lengths on it, is**

(a) 2x-2y-3=0

(b) 2x-2y+3=0

(c) x-y+6=0

(d) x -y -6=0

## Answer

A

**Question: The equation of the tangents drawn from the origin**

## Answer

(A,C)

**Question: The equation of a circle C _{1} is x^{2}+y^{2}=4. The locus of the intersection of orthogonal tangents to the circle is the curve C_{2} and the locus of the intersection of perpendicular tangents to the curve C_{2 }is the curve C_{3 }.Then,**

(a) C

_{3}is a circle

(b) the area enclosed by the curve C

_{3 }is 8π

(c) C

_{2}and C

_{3}are circles with the same centre

(d) None of the above

## Answer

(A,C)

**Question: A (1/√2,1/√2) is a point on the circle x ^{2}+y^{2}=1 and B is another point on the circle such that arc length AB =π/2 units. Then, coordinates of B can be**

(a) (1/√2,-1/2)

(b) (-1/√2,1/√2

(c) (−1/√2,-1/√2)

(d) None of these

## Answer

(A,B)

**Question. Find the equation of the ellipse whose foci are (2, 3), (–2, 3) and whose semi-minor axis is of length 5.**

(a) 5x^{2} + 9y^{2} + 54y + 36 = 0

(b) 5x^{2} + 9y^{2} – 54y + 36 = 0

(c) 5x^{2} + 9y^{2} – 54y – 36 = 0

(d) None of these

## Answer

B

**Question. The position of the point(4, – 3)relative to an ellipse x2/28 + y2/20 = 1 is**

(a) inside

(b) on the ellipse

(c) outside

(d) cannot say

## Answer

C

**Question. A tangent at any point to the ellipse 4x ^{2 }+ 9y^{2} = 36 is cut by the tangent at the extremities of the major axis at T and T’. The circle on T T’ as diameter passes through the point**

(a) (0, √5 )

(b) ( √5, 0)

(c) (2, 1)

(d) (0, – √5 )

## Answer

B

**Question. If the normal at point P on the ellipse x ^{2}/a^{2 }+ y^{2}/b^{2} = 1 meets the axes in R and S respectively, then PR : RS is equal to**

(a) a : b

(b) a

^{2}: b

^{2}

(c) b

^{2}: a

^{2}

(d) b : a

## Answer

C

**Question. An ellipse is described by using endles string which is passed over two pins. If the axes are 6 cm and 4 cm, the necessary length of the string and distance between the pins respectively in cm, are**

(a) 6, 2√5

(b) 6, √5

(c) 4, 2√5

(d) None of these

## Answer

D

**Question. The equation of the normal at the point (2, 3) on the ellipse 9x ^{2} + 16y^{2} = 180 is**

(a) 3y = 8x -10

(b) 3y – 8x + 7 = 0

(c) 8y + 3x + 7 = 0

(d) 3x + 2y + 7 = 0

## Answer

B

**Question. The curve represented by x = 3(cos t + sin t)and y = 4(cos t – sin t) is**

(a) ellipse

(b) parabola

(c) hyperbola

(d) circle

## Answer

A

**Question. On the ellipse 4x ^{2} + 9y^{2} = 1, the point at which the tangent is parallel to the line 8x = 9y, is**

(a) (2/5 , 1/5)

(b) (-2/5 , 1/5)

(c) (-2/5 , -1/5)

(d) None of these

## Answer

B

**Question. An equation of the normal to the ellipse x2/a2 + y ^{2}/b2 = 1at the positive end of the latusrectum is**

(a) x + ey + e

^{3}a = 0

(b) x – ey – ae

^{3}= 0

(c) x – ey + e

^{3}a = 0

(d) x + ey – e

^{3}a = 0

## Answer

B

**Question. The circle x ^{2} + y^{2} = c^{2} contains the ellipse x^{2}/a^{2} + y^{2}/b^{2} = 1, if**

(a) c < a

(b) c < b

(c) c > a

(d) c > b

## Answer

C

**Question. If Qbe the point on the auxiliary circle corresponding to a point P on an ellipse. Then, the normals at P and Q meet on**

(a) a fixed circle

(b) an ellipse

(c) a hyperbola

(d) None of these

## Answer

A

**Question. If the tangent line to an ellipse x2/a2 + y ^{2}/b2 = 1 1cuts intercepts h and k from axes, then a2/h2 + b2/k2 is equal to**

(a) 0

(b) 1

(c) -1

(d) 2

## Answer

B

**Question. If the latusrectum of an ellipse is equal to half of minor axis, then its eccentricity is**

(a) √15/3

(b) √15/2

(c) √15/6

(d) √15/4

## Answer

D

**Question. If the eccentricity of an ellipse is 5/8 and the distance between its foci is 10, then length of latus rectum of the ellipse is**

(a) 39/7

(b) 39/4

(c) 39/5

(d) 39/8

## Answer

B

**Question. The locus of mid-points of chords of the ellipse x ^{2}/a^{2} + y^{2}/b^{2} = 1 that touch the circle x^{2} + y^{2} = b^{2}, is**

(a) ( x

^{2}/a

^{2}+ y

^{2}/b

^{2}) = x

^{2}/a

^{4}+ y

^{2}/b

^{4}

(b) ( x

^{2}/a

^{2}+ y

^{2}/b

^{2}) =b

^{2}(x

^{2}/a

^{4}+ y

^{2}/b

^{4})

(c) ( x

^{2}/a

^{2}+ y

^{2}/b

^{2}) = b

^{2}(x

^{2}/a

^{4}+ y

^{2}/b

^{4})

(d) None of these

## Answer

B

**Question. The eccentric angles of the extremities of latusrectum of the ellipse x ^{2}/a^{2} + y^{2}/b^{2} = 1 are given by**

(a) tan-1 (± ac/b)

(b) tan-1 (± bc/a)

(c) tan-1 (± b/ae)

(d) tan-1 (± a/be)

## Answer

C

**Question. If the two tangents drawn to the ellipse x ^{2}/a^{2 }+ y^{2}/b^{2} = 1 intersect perpendicularly at p, then locus of p is a circle x^{2 }+ y^{2} = a^{2} + b^{2}. Then, the circle is called**

(a) auxiliary circle

(b) director circle

(c) great circle

(d) None of these

## Answer

B

**Question. An ellipse is sliding along the coordinate axes. If the foci of the ellipse are (1, 1) and (3, 3), then area of the director circle of the ellipse is**

(a) 2π sq units

(b) 4π sq units

(c) 6π sq units

(d) 8π sq units

## Answer

D

**Question. The eccentric angle of a point on the ellipse x ^{2}/6 + y^{2}/2 = 1 whose distance from the centre of the ellipse is 2, is**

(a) π/4

(b) 3π/2

(c) 5π/3

(d) 7π/6

## Answer

A

**Question. If e is eccentricity of ellipse x ^{2}/a^{2 }+ y^{2}/b^{2} = 1 (a > b) and e’ is eccentricity of x^{2}/a^{2 }+ y^{2}/b^{2} = 1 (a < b) , then**

(a) e = e’

(b) ee’ = 1

(c) 1/e

^{2}+ 1/(e’)

^{2}= 1

(d) None of these

## Answer

C

**Question. If the normals atP(q)and Q(π/2 +θ) to the ellipse x ^{2}/a^{2} + y^{2}/b^{2} = 1 meet the major axis at Gand grespectivel,y the PG^{2} + Qg^{2} is equal to**

(a) b

^{2}(1- e

^{2})(2 – e

^{2})

(b) b

^{2}(e

^{4}– e

^{2}+ 2)

(c) a2(1+ e

^{2})(2 + e

^{2})

(d) b

^{2}(1+ e

^{2})(2 + e

^{2})

## Answer

B

**Question. If ax ^{2} + by^{2} + 2hxy + 2gx + 2fy + c = 0 (abc + 2fgh – af^{2} – bg^{2} – ch^{2} ≠ 0) represents an ellipse, if**

(a) h

^{2}= ab

(b) h

^{2}>ab

(c) h

^{2}< ab

(d) None of these

## Answer

C

**Question. The equation of the ellipse whose focus is (1, –1), the directrix of line x – y – 3 = 0 and eccentricity 1/2 is**

(a) 7x^{2} + 2xy + 7y^{2} – 10x + 10y + 7 = 0

(b) 7x^{2} + 2xy + 7y^{2} + 7 = 0

(c) 7x^{2} + 2xy + 7y^{2} – 10x + 10y – 7 = 0

(d) None of the above

## Answer

A

**Question. The length of the latusrectum of the ellipse 3x ^{2} + y^{2} = 12 is**

(a) 4

(b) 3

(c) 8

(d) 4/√3

## Answer

D

**Question. If e is the eccentricity of the ellipse x ^{2}/a^{2} + y^{2}/b^{2} = 1 (a < b), then**

(a) b

^{2}= a

^{2}(1 -e

^{2})

(b) a

^{2}= b

^{2}(1 -e

^{2})

(c) a

^{2}= b

^{2}= (e

^{2}– 1)

(d) b

^{2}= a

^{2}= (e

^{2}– 1)

## Answer

B

**Question. If Pis a point on the ellipse x ^{2}/16 + y^{2}/25 = 1 1whose foci are S and S’, then PS + PS’ is equal to**

(a) 8

(b) 7

(c) 5

(d) 10

## Answer

D

**Question. The locus of a point which moves such that the sum of its distances from two fixed points is always a constant, is**

(a) a straight line

(b) a circle

(c) an ellipse

(d) a hyperbola

## Answer

C

**Question. Find the distance between the directrices of the ellipse x ^{2}/36 + y^{2}/20 = 1.**

(a) -18

(b) 18

(c) 17

(d) 19

## Answer

B

**Question. If equation of ellipse is x ^{2}/4 + y^{2}/25 = 1 , then coordinate of the foci, eccentricity and the length of the latusrectum are respectively**

(a) (0,± √21), √21/5 , 7/5

(b) (0,± √21), √21/5 , 8/5

(c) (0,± √21), √21/7 , 8/5

(d) None of the above

## Answer

B

**Question. If p, q are the segments of a focal chord of an ellipse b ^{2}x^{2 }+ a^{2}y^{2} = a^{2}b^{2}, then**

(a) a

^{2}( p+q ) = 2bpq

(b) b

^{2}( p+q ) = 2apq

(c) a( p+q ) = 2b

^{2}pq

(d) b( p+q ) = 2a

^{2}pq

## Answer

B

**Question. The equation of the ellipse whose foci are (±2, 0) and eccentricity 1/2, is**

(a) x^{2}/12 + y^{2}/16 = 1

(b) x^{2}/16 + y^{2}/12 = 1

(c) x^{2}/16 + y^{2}/8 = 1

(d) None of these

## Answer

B

**Question. If vertices and foci of an ellipse are (0, ± 13) and (0, ± 5) respectively, then the equation of an ellipse is**

(a) x^{2}/144 + y^{2}/169 = 1

(b) x^{2}/169 + y^{2}/144 = 1

(c) x^{2}/12+ y^{2}/13= 1

(d) None of these

## Answer

A

**Question. Find the equation of an ellipse, if major axis on the x-axis and passes through the points (4, 3) and (6, 2).**

(a) x^{2}/13+ y^{2}/52= 1

(b) x^{2}/40+ y^{2}/10= 1

(c) x^{2}/52+ y^{2}/13= 1

(d) None of these

## Answer

C

**Question. The curve with parametric equations x = α + 5cos q, y = β + 4 sin q (where, q is parameter) is**

(a) a parabola

(b) an ellipse

(c) a hyperbola

(d) None of these

## Answer

B

**Question. The curve represented by the equation 4x ^{2} + 16y^{2} – 24x – 32y – 12 = 0 is**

(a) a parabola

(b) a pair of straight lines

(c) an ellipse with eccentricity 1/2

(d) an ellipse with eccentricity √3/2

## Answer

D

**Question. In an ellipse length of minor axis is 8 and eccentricity is √5/3. The length of major axis is**

(a) 6

(b) 12

(c) 10

(d) 16

## Answer

B

**Question. In an ellipse the distance between the foci is 8 and the distance between the directrices is 25. The length of major axis is**

(a) 10√2

(b) 20√2

(c) 30√2

(d) None of these

## Answer

A

**Question. If the eccentricity of the two ellipse x ^{2}/169 + y^{2}/25 = 1 and x^{2}/a^{2 }+ y^{2}/b^{2} = 1 are equal, then the value of a/b is**

(a) 5/13

(b) 6/13

(c) 13/5

(d) 13/6

## Answer

C

**Question. The line x = at ^{2} meets the ellipse x^{2}/a^{2 }+ y^{2}/b^{2} = 1 in the real points, if**

(a) |t | < 2

(b) | t | ∈ 1

(c) |t | > 1

(d) None of these

## Answer

B

**Question. The angle between the pair of tangents drawn from the point (1, 2) to the ellipse 3x ^{2} + 2y^{2} = 5 , is**

(a) tan

^{-1}(12 /5)

(b) tan

^{-1}(6/ √5)

(c) tan

^{-1}(2 /√5)

(d) tan

^{-1 }(6 /5)

## Answer

C

**Question. If x cos α + y sin α = pis a tangent to the ellipse, then**

(a) a^{2} sin α +b^{2} cosα = p^{2}

(b) a^{2} + b^{2}sin^{2}α = p^{2} cosec^{2}α

(c) a^{2} + cos^{2}α = b^{2}sin^{2}α = p^{2}

(d) None of the above

## Answer

C

**Question. Number of tangents from (7, 6) to ellipse x ^{2}/16 + y^{2}/25 = 1 is**

(a) 0

(b) 1

(c) 2

(d) None of these

## Answer

C

**Question. Let E be the ellipse x ^{2}/9 + y^{2}/4 = 1 and C be the circle x^{2} + y^{2} = 9. Let P andQbe the points (1, 2) and (2, 1), respectively. Then,**

(a) Q lies inside C but outside E

(b) Q lies outside both C and E

(c) P lies inside both Cand E

(d) P lies inside C but outside E

## Answer

B

**Question. The length of the axes of the conic 9x ^{2} + 4y^{2} – 6x + 4y +1 = 0**

(a) 1/2,9

(b) 3, 2/5

(c) 1, 2/3

(d) 3, 2

## Answer

C

**Question. The distance of the centre of ellipse x ^{2} + 2y^{2} – 2 = 0 to those tangents of the ellipse which are equallyinclined from both the axes, is**

(a) 3/√2

(b) √(3/2)

(c) √2/3

(d) √3/2

## Answer

D

**Question. The distances from the foci of P(x , y ) 1 1 on the ellipse x ^{2}/9 + y^{2}/25 = 1 are**

(a) 4 ± 5/4 y1

(b) 5 ± 4/5 x1

(c) 5 ± 4/5 y1

(d) None of these

## Answer

C

**Question. The sum of focal distance of any point on the ellipse with major and minor axes as 2a and 2b respectively, is equal to**

(a) 2a

(b) 2 a/b

(c) 2 b/a

(d) b/a

## Answer

A

**Question. The locus of the point of intersection of the perpendicular tangents to the ellipse x ^{2}/9+ y^{2}/4= 1 is**

(a) x

^{2 }+ y

^{2}= 9

(b) x

^{2 }+ y

^{2}= 4

(c) x

^{2 }+ y

^{2}= 13

(d) x

^{2 }+ y

^{2}= 5

## Answer

C

**Question. The number of circle having radius 5 and passing through the points (– 2, 0) and (4, 0) is:**

(a) One

(b) Two

(c) Four

(d) Infinite

## Answer

B

**Question. The locus of the centre of the circle which cuts off intercepts of length 2a and 2b from x-axis and y-axis respectively, is:**

(a) x + y = a + b

(b) x^{2} + y^{2} = a^{2} + b^{2}

(c) x^{2} − y^{2} = a^{2} − b^{2}

(d) x^{2} + y^{2} = a^{2} − b^{2}

## Answer

C

**Question. The equations to the tangents to the circle x ^{2} + y^{2} − 6x + 4y =12 which are parallel to the straight line 4x+3y+5=0, are:**

(a) 3x − 4y −19 = 0, 3x − 4y + 31 = 0

(b) 4x + 3y −19 = 0, 4x + 3y + 31 = 0

(c) 4x + 3y +19 = 0, 4x + 3y − 31 = 0

(d) 3x − 4y +19 = 0, 3x − 4y + 31 = 0

## Answer

C

**Question. The equations of any tangents to the circle x ^{2} + y^{2} − 2x + 4y − 4 = 0 is:**

(a) y = m(x −1) + 3 √1+ m

^{2}− 2

(b) y = mx + 3 √1+ m

^{2}

(c) y = mx + 3 √1+ m

^{2}− 2

(d) None of these

## Answer

A

**Question. If the distances from the origin to the centres of three circles x ^{2} + y^{2} + 2λ_{1}x −C^{2} = 0 ( 1,2,3) i x + y + λ x − c = i = are in G.P. then the lengths of the tangents drawn to them from any point on the circle x^{2} + y^{2} = c^{2} are in:**

(a) (a)P.

(b) G.P.

(c) H.P.

(d) None of these

## Answer

B

**Question. The angle between a pair of tangents drawn from a point P to the circle x ^{2} + y^{2} + 4x − 6 y + 9sin α +13cos α = 0 is 2α The equation of the locus of the point P is:**

(a) x

^{2}+ y

^{2}+ 4x − 6y + 4 = 0

(b) x

^{2}+ y

^{2}+ 4x − 6y − 9 = 0

(c) x

^{2}+ y

^{2}+ 4x − 6y − 4 = 0

(d) x

^{2}+ y

^{2}+ 4x − 6y + 9 = 0

## Answer

D

**Question. The line lx + my + n = 0 is a normal to the circle x ^{2} + y^{2} + 2gx + 2 fy + c = 0, if:**

(a) lg+ mf − n = 0

(b) lg+ mf + n = 0

(c) lg−mf − n = 0

(d) lg−mf + n = 0

## Answer

A

**Question. If the circle x ^{2} + y^{2} +2gx+2fy+c =0cuts each of the circle x^{2} + y^{2} −4 = 0, x^{2} + y^{2} −6x−8y+10=0 and x^{2} + y^{2} +2x−4y−2=0 at the extremities of a diameter, then **

(a) c = −4

(b) g + f = c −1

(c) g

^{2}+ f

^{2}− c =17

(d) g f = 6

## Answer

All

**Question. Equation of the circle having diameter x − 2 y + 3 = 0, 4 x − 3 y + 2 = 0 and radius equal to 1 is **

(a) (x −1)^{2} + ( y − 2)^{2} =1

(b) (x − 2)^{2} + ( y −1)^{2} =1

(c) x^{2} + y^{2} − 2x − 4y + 4 = 0

(d) x^{2} + y^{2} −3x − 4y + 7 = 0

## Answer

A,B

**Question. Tangents are drawn from any point on the circle x ^{2} + y^{2} = a^{2} to the circle x^{2} + y^{2} = b^{2} . If the chord of contact touches the circle x^{2} + y^{2} = c^{2} , a > b, then: **

(a) a, b, c are in (a)P.

(b) a, b, c are in G.P.

(c) a, b, c are in H.P.

(d) a, c, b are in G.P.

## Answer

B

**Question. If two distinct chords, drawn from the point (p, q) on the circle x ^{2} + y^{2 }= px + qy (where p, q ≠ 0) are bisected by the x-axis, then:**

(a) p

^{2}= q

^{2}

(b) p

^{2}= 8q

^{2}

(c) p

^{2}< 8q

^{2}

(d) p

^{2}> 8q

^{2}

## Answer

D

**Question. The common chord of the circle x ^{2} + y^{2} + 4x +1 = 0 and x^{2} + y^{2} + 6x + 2y + 3 = 0 is:**

(a) x + y +1 = 0

(b) 5x + y + 2 = 0

(c) 2x + 2y + 5 = 0

(d) 3x + y + 3 = 0

## Answer

A

**Question. The equation of the chord of the circle x ^{2} + y^{2} = a having (x1 , y1 ) as its mid-point is: **

(a) xy

_{1}+ yx

_{1}= a

^{2}

(b) x

_{1}+ y

_{1}= a

(c) xx

_{1}+ yy

_{1}= x

_{1}

^{2}+ y

_{1}

^{2}

(d) xx

_{1}+ yy

_{1}= a

^{2}.

## Answer

C

**Question. A circle of radius 5 units touches both the axes and lies in first quadrant. If the circle makes one complete roll on xaxis along the positive direction of x-axis, then its equation in the new position is:**

(a) x^{2} + y^{2} + 20π x −10y +100π = 0

(b) x^{2} + y^{2} + 20π x +10y +100π = 0

(c) x^{2} + y^{2} − 20π x −10 y +100π = 0

(d) None of these

## Answer

D

**Question. If the line x + 2by + 7 = 0 is a diameter of the circle x ^{2} + y^{2} − 6x + 2y = 0, then b = ?**

(a) 3

(b) –5

(c) –1

(d) 5

## Answer

B