Students can refer to the following Conic Sections MCQ Questions for Class 11 Maths with Answers provided below based on the latest curriculum and examination pattern issued by CBSE and NCERT. Our teachers have provided here a collection of multiple choice questions for Conic Sections Class 11 covering all topics in your textbook so that students can assess themselves on all important topics and thoroughly prepare for their exams

**Conic Sections MCQ Questions for Class 11 Maths with Answers**

We have provided below Conic Sections MCQ Questions for Class 11 Maths with answers which will help the students to go through the entire syllabus and practice multiple choice questions provided here with solutions. As Conic Sections MCQs in Class 11 Mathematics pdf download can be really scoring for students, you should go through all problems provided below so that you are able to get more marks in your exams.

**Question. If one end of a diameter of the circle x ^{2} + y^{2} – 4x – 6y + 11 = 0 is (3, 4), then find the coordinate of the other end of the diameter.**

(a) (2, 1)

(b) (1, 2)

(c) (1, 1)

(d) None of these

## Answer

B

**Question. The centre of a circle is (2, – 3) and the circumference is 10p. Then, the equation of the circle is**

(a) x^{2} + y^{2} + 4x + 6y +12 = 0

(b) x^{2} + y^{2} – 4x + 6y +12 = 0

(c) x^{2} + y^{2} – 4x + 6y -12 = 0

(d) x^{2} + y^{2} – 4x – 6y -12 = 0

## Answer

C

**Question: If the vertex of a parabola is the point(-3,0 ) and the directrix is the line x +5= 0, then equation of parabola is**

(a) y^{2}=8(x+3) x 2

(b) x^{2}=8(y+3)

(c) y^{2}=-8(x+3 x 2

(d) y^{2}=8(x+5) x 2

## Answer

A

**Question: The focus of the parabola y ^{2}=4y-4x is**

(a) (0, 2)

(b) (1, 2)

(c) (2, 0)

(d) (2, 1)

## Answer

A

**Question: The equation λx ^{2}+4xy+y^{2}+ λx+3y+2=0 parabola, if λ is**

(a) -4

(b) 4

(c) 0

(d) None of these

## Answer

B

**Question: The length of latusrectum of the parabola 169 {(x-1) ^{2}+(y-3)^{2}}=(5x-12y+17)^{2} is**

(a) 14/13

(b) 28/13

(c) 12/13

(d) None of these

## Answer

B

**Question: The latusrectum of the parabola y ^{2}=5x+4y+1 is**

(a) 5/4

(b) 10

(c) 5

(d) 5/2

## Answer

A

**Question: The equation of parabola having vertex ( , )0 0 , passing through (5 , 2) and symmetric with respect to y-axis is**

(a) 3x^{2}=25y

(b) 2x^{2}=25y

(c) 2y^{2}=25x

(d) None of these

## Answer

B

**Question: x -2=t ^{2},y=2t are the parametric equations of the parabola**

(a) y

^{2}=4x

(b) y

^{2}==-4x

(c) x

^{2}=-4y

(d) y

^{2}==4(x-2)

## Answer

D

**Question: If the point P(4,2) is one end of the focal chord PQ of the parabola y ^{2}=x, then the slope of the tangent at Q is**

(a) -1/4

(b) 1/4

(c) 4

(d) -4

## Answer

C

**Question: The equation of the parabola having vertex at the origin axis on the y-axis and passing through the point(6 ,3) is**

(a) y^{2}=12x+6

(b) x^{2}=12y y 2

(c) x^{2}=-12y

(d) y^{2}=-12x+6

## Answer

C

**Question: The tangents and normal at the ends of the latusrectum of a parabola form a**

(a) cyclic quadrilateral

(b) rectangle

(c) square

(d) None of these

## Answer

C

**Question: The locus of the middle points of the focal chords of parabola**

y2=4ax is

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

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

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

(d) None of these

## Answer

B

**Question: If the normal to the parabola y ^{2}=4ax at the point P(at^{2}, 2at) cuts the parabola again at Q(aT^{2},2aT aT), then**

(a) – 2≤ T ≤2

(b) T∈(-∞,-8) ∪ (8,∞)

(c) T

^{2 }< 8

(d) T

^{2 }≤ 8

## Answer

D

**Question: A tangent to a parabola y2=4 ax is inclined at π/3 with the axis of the parabola. The point of contact is**

## Answer

A

**Question: If tangents at A and B on the parabola y ^{2}=4ax intersect at point C,then ordinates of A C, and B are**

(a) always in AP

(b) always in GP

(c) always in HP

(d) None of these

## Answer

A

**Question: The equation of tangent to the parabola y ^{2}=9x x 2 which goes throughthe point (4, 10), is**

(a) x+4y+1=0

(b) 9x+4y+4=0

(c) x-4y+36=0

(d) 9x+4y+9=0

## Answer

C

**Question: The tangent to the parabola y ^{2}=4ax at the point( a,2a) makes with x-axis an angle equal to**

(a) π/3

(b) π/4

(c) π/2

(d)π/6

## Answer

B

**Question: If the tangent at the point P(2,) 4 to the parabola y ^{2}=8x meets the parabola y^{2}=8x+5ay Q and R, then the mid-point of the QR is**

(a) (2, 4)

(b) (4,2)

(c) (7, 9)

(d) None of these

## Answer

B

**Question: At what point on the parabola y ^{2}=4x,the normal makes equal angles with the coordinate axes?**

(a) (4, 4)

(b) (9, 6)

(c) (4,-4)

(d) (1,-2)

## Answer

D

**Question: The circle x ^{2}+y^{2}=5 meets the parabola y^{2}=4x at P and Q . Then, the length PQ is equal to**

(a) 2

(b) 2√2

(c) 4

(d) None of these

## Answer

C

**Question: The normal at three points P, Q, R of the parabola y ^{2}=4ax meet in (h k). The centroid of Δ PQR lies on**

(a) x = 0

(b) y = 0

(c) x=-a

(d) y=a

## Answer

B

**Question. If the tangent at the point P on the circle x ^{2} + y^{2} + 6x + 6y= 2 meets the straight line 5x – 2y + 6 = 0 at a point Q on the y-axis, then the length of PQ is**

(a) 4

(b) 2√5

(c) 5

(d) 3√5

## Answer

C

**Question. If the abscissae and ordinates of two points P and Q are roots of the equations x ^{2} + 2ax – b^{2} = 0 and y^{2} + 2py – q^{2} = 0 respectively, then the equation of**

**the circle with PQ as diameter, is**

(a) x

^{2}+ y

^{2}+ 2ax + 2py – b

^{2}– q

^{2}= 0

(b) x

^{2}+ y

^{2}– 2ax – 2py + b

^{2}+ q

^{2}= 0

(c) x

^{2}+ y

^{2}– 2ax – 2py – b

^{2}– q

^{2}= 0

(d) x

^{2}+ y

^{2}– 2ax + 2py + b

^{2}+ q

^{2}= 0

## Answer

A

**Question. The line 3x – 2y = kmeets the circle x ^{2} + y^{2} = 4r^{2} at only one point, if k^{2} is**

(a) 20 r

^{2}

(b) 52 r

^{2}

(c) 52/9 r

^{2}

(d) 20/9 r

^{2}

## Answer

B

**Question. A line through (0, 0) cuts the circle x ^{2} + y^{2}– 2ax = 0 at A and B, then locus of the centre of the circle drawn AB as diameter is**

(a) x

^{2}+ y

^{2}– 2ay = 0

(b) x

^{2}+ y

^{2}+ ay = 0

(c) x

^{2}+ y

^{2}+ ax = 0

(d) x

^{2}+ y

^{2}– ax = 0

## Answer

D

**Question. Let PQand PS be tangents at the extremities of the diameter PR of a circle of radius r. If PS and RQ intersect at a point x on the circumference of the circle, then 2r equals**

(a) √(PQ × RS)

(b) PQ + RS/2

(c) 2PQ . RS/PQ + RS

(d) (PQ^{2} . RS^{2} )/2

## Answer

A

**Question. If (a cos Θi , a sin Θi) , i = 1, 2, 3 represent the vertices of an equilateral triangle inscribed in a circle, then **

(a) cos Θ_{1} cos Θ_{2} cosΘ_{3} = 0

(b) sec Θ_{1} sec Θ_{2} secΘ_{3} = 0

(c) tan Θ_{1} tan Θ_{2} tanΘ_{3} = 0

(d) cot Θ_{1} cot Θ_{2} cotΘ_{3} = 0

## Answer

A

**Question. The range of a, for which the point (a, a) lies inside the region bounded by the curves y = √1 – x ^{2} and x + y = 1 is**

(a) 1/2 < α < 1/√2

(b) 1/2 < α < 1/3

(c) 1/3 < α < 1/√3

(d) 1/4 < α < 1/2

## Answer

A

**Question. A line meets the coordinate axes in A and B.A circle is circumscribed about the DOAB. The distances from the points A and Bof the side ABto the tangent at O are equal to mand n 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 L1 be a straight line passing through the origin and L2 be the straight line x + y = 1. If the intercepts made by the circle x ^{2} + y^{2} – x + 3y = 0 on L_{1}L_{2} and are equal, then L1 can be represented by**

(a) x + y = 0

(b) x – y = 0

(c) 7x + y = 0

(d) x – 7y = 0

## Answer

B

**Question. The set of values of c so that the equations y =|x|+ c and x ^{2} + y^{2} – 8|x|- 9 = 0 have no solution, is**

(a) (-∞, – 3) È (3, ∞)

(b) (-3, 3)

(c) (-∞, 5 2) È (5 2, ∞)

(d) (5 2 – 4, ∞)

## Answer

D

**Question. The range of values of a such that the angle q 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. Two points P and Qare taken on the line joining the points A(0 ,0) and B(3a, 0) such that AP = PQ = QB.****Circles are drawn on AP, PQand QB as diameters.****The locus of the points, the sum of the squares of the tangents from which to the three circles is equal to b2, is**

(a) x^{2} + y^{2 }– 3ax + 2a^{2} – b^{2} = 0

(b) 3x^{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. 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 y = 0

(d) 7x – 24 y = 0

## Answer

B

**Question. In a ΔABC, 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) AB x AD /√(AB^{2} x AD^{2})

(b) AB x AD /AB + AD

(c) √(AB x AD)

(d) AB x AD /√(AB^{2} – AD^{2})

## Answer

D

**Question. Two perpendicular tangents to the circle x ^{2} + y^{2} = a^{2} meet at P. Then, the locus of P has the equation**

(a) x

^{2}+ y

^{2}= 2a

^{2}

(b) x

^{2}+ y

^{2}= 3a

^{2}

(c) x

^{2}+ y

^{2}= 4a

^{2}

(d) None of these

## Answer

A

**Question. From a point on the circle x ^{2} + y^{2} = a^{2}, two tangents are drawn to the circle x^{2} + y^{2} = a^{2} sin2α.The angle between them is**

(a) α

(b) α/2

(c) 2α

(d) None of these

## Answer

C

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

(a) (-6, 11)

(b) (-9, -13)

(c) (-10, -15)

(d) (-6, -7)

## Answer

D

**Question. The equation x ^{2} + y^{2} + 2gx + 2fy + c = 0 will represent a real circle, if**

(a) g

^{2}+ f

^{2}– c < 0

(b) g

^{2}+ f

^{2}– c ≥ 0

(c) always

(d) None of these

## Answer

B

**Question. The tangents to x ^{2} + y^{2} = a^{2} having inclinationsa andbintersect at P. If cot a + cot b = 0, then the locus of P is**

(a) x + y = 0

(b) x – y = 0

(c) xy = 0

(d) None of these

## Answer

C

**Question. The equation of a line inclined at an angle p/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 a circleC _{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 8p

(c) C

_{2}and C

_{3}are circles with the same centre

(d) None of the above

## Answer

(a,c)

**Question. The equation of the tangents drawn from the origin to the circle x ^{2} + y^{2 }– 2rx – 2hy + h^{2} = 0, are**

(a) x = 0

(b) y = 0

(c) (h

^{2}– r

^{2})x – 2rhy = 0

(d) (h

^{2}– r

^{2})x + 2rhy = 0

## Answer

(a,c)

**Question. If P = (2, 3), then the centre of circumcircle of ΔQRS is**

(a) (2/13 .7/26)

(b) (2/13 .3/26) **(c) (3/13 .9/26) **

(d) (3/13 .2/13)

## Answer

C

**Question. The circle passing through (1, -2) and touching the axis to x at (3, 0) also passes through the point**

(a) (-5,2)

(b) (2, -5)

(c) (5, – 2)

(d) (-2,5)

## Answer

C

**Question**. **If a > 2 b > 0, then the positive value of m for which y = mx – b√(1 + m ^{2}) is a common tangent to x^{2} + y^{2} = b^{2} and (x – a)^{2} + y^{2} = b^{2}, is**

## Answer

A

**Question. The length of the diameter of the circle which touches the x-axis at the point (1, 0) and passes through the point (2, 3) is **

(a) 10/3

(b) 3/5

(c) 6/5

(d) 5/3

## Answer

A

**Question. The two circles x y ax 2 + 2 = and x y c 2 + 2 = 2, (c > 0) touch each other if **

(a) |a |= c

(b) a = 2c

(c) |a |= 2c

(d) 2|a |= c

## Answer

A

**Question. The equation of the circle passing through the points (1,0) and (0, 1) and having the smallest radius is**

(a) x^{2} + y^{2 }+x + y – 2 = 0

(b) x^{2} + y^{2 }-2x – 2y + 1 = 0

(c) x^{2} + y^{2 }-x – y = 0

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

## Answer

C

**Question. The point diameterically opposite to the point P(1, 0) on the circle x ^{2} + y^{2 }+2x + 2y – 3 = 0 is**

(a) (3, 4)

(b) (3, – 4)

(c) (- 3, 4)

(d) (- 3, – 4)

## Answer

D

**Question. Consider a family of circles which are passing through the point (- 1, 1) and are tangent to x-axis. If (h, k) is the centre of circle, then **

(a) k ≥ 1/2

(b) – 1/2 ≤ k ≤ 1/2

(c) k ≤ 1/2

(d) 0 < k < 1/2

## Answer

A

**Question. Any chord of the circle x ^{2} + y^{2} = 25 subtends a right angle at the centre. Then, the locus of the centroid of the triangle made by the chord and a moving point P on the circle is**

(a) parabola

(b) circle

(c) rectangular hyperbola

(d) ellipse

## Answer

B

**Question. LetC be the circle with centre (0, 0) and radius 3. The equation of the locus of the mid-points of the chords of the circleC that subtend an angle 2p/3 at its centre is**

(a) x^{2} + y^{2 }=27/4

(b) x^{2} + y^{2 }=9/4

(c) x^{2} + y^{2 }=3/2

(d) x^{2} + y^{2 }=1

## Answer

B

**Question. If the lines 3x – 4 y – 7 = 0 and 2x – 3 y – 5 = 0 are two diameters of a circle of area 49p sq units, the equation of the circle is **

(a) x^{2} + y^{2 }=2x – 2y – 62 = 0

(b) x^{2} + y^{2 }=2x + 2y – 62 = 0

(c) x^{2} + y^{2 }=2x + 2y – 47 = 0

(d)x^{2} + y^{2 }=2x – 2y – 47 = 0

## Answer

C

**Question. If the pair of lines ax ^{2} + 2(a+b)xy + by2 = 0 lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sectors is thrice the area of another sector, then **

(a) 3a

^{2}+ 2ab + 3b

^{2}= 0

(b) 3a

^{2}+ 10ab + 3b

^{2}= 0

(c) 3a

_{2}– 2ab + 3b

^{2}= 0

(d) 3a

^{2}– 10ab + 3b

^{2}= 0

## Answer

A

**Question. A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius 2. The locus of the centre of the circle is **

(a) a parabola

(b) a hyperbola

(c) a circle

(d) an ellipse

## Answer

A

**Question. The intercept on the line y = x by the circle x ^{2} + y^{2} – 2x = 0 is AB. Equation of the circle on ABas a diameter is **

(a) x

^{2}+ y

^{2}– x – y = 0

(b) x

^{2}+ y

^{2}– x + y = 0

(c) x

^{2}+ y

^{2}+ x + y = 0

(d) x

^{2}+ y

^{2}+ x – y = 0

## Answer

A

**Question. How many common tangents can be drawn to the following circles x ^{2} + y^{2} = 6 and x^{2} + y^{2} + 6x + 2y + 1 = 0 ? **

(a) 4

(b) 3

(c) 2

(d) 1

## Answer

A

**Question. The circle x ^{2} + y^{2} – 10x – 14 y + 24 = 0 cuts an intercepts on y-axis of length**

(a) 5

(b) 10

(c) 1

(d) None of these

## Answer

B

**Question. If the line 3x – 4 y – k = 0, (k > 0) touches the circle x ^{2} + y^{2} – 4x + 10y + 5 = 0= 0 at (a, b) , then k + a + b is equal to**

(a) 20

(b) 22

(c) -30

(d) -28

## Answer

A

**Question. A variable circle passes through the fixed point A( p, q) and touches x-axis. The locus of the other end of the diameter through A is **

(a) (x – p)^{2} = 4qy

(b) (x – q)^{2} = 4py

(c) ( y – p)^{2} = 4qx

(d) ( y – q)^{2} = px

## Answer

A

**Directions (Q. Nos. 21- 27) Each of these questions contains two statements : Statement I (Assertion) and Statement II (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select one of the codes (a), (b), (c) and (d) given below.**

(a) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.

(b) Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.

(c) Statement I is true; Statement II is false.

(d) Statement I is false; Statement II is true.

**Question**. Statement I Circles x^{2} + y^{2} = 4 and x^{2} + y^{2} – 8x + 7 = 0**intersect each other at two distinct points.****Statement **II Circles with centresC1 andC2 and radii r_{1 }and r_{2} intersect at two distinct points, if |C_{1} C_{2} |<r_{1} r_{2} . ** **

## Answer

C

**Question. Let C _{1}C_{2} and be two circles with C_{2} lying inside C_{1}. ** A circle C lying inside C

Statement I

_{1}touches C

_{1}internally and C

_{2}externally. Then, the locus of the centre of C is an ellipse.

**Statement II**If A and B are foci and P be any point on the ellipse, then AP + BP = constant.

## Answer

A

**Question**. **Statement** **I** Number of circles passing through (- 2, 1), (- 1, 0), (- 4, 3) is 1.**Statement II** Through three non-collinear points in a plane only one circle can be drawn. ** **

## Answer

D

**Question**. **Consider two circlesS ≡ x ^{2} + y^{2} + 2gx + 2fy = 0and S’ ≡ x^{2} + y^{2} + 2g’ x + 2f’y = 0 **

**Statement I**If two circles S and S¢ touch each other, then f < g = fg< .

**Statement II**Two circles touch each other, if line joining their centres is perpendicular to all possible common tangents.

## Answer

B

**Question**. **Statement I** Circle x^{2} + y^{2} – 6x – 4y + 9 = 0 bisects the circumference of the circle x^{2} + y^{2} – 8x – 6y + 23 = 0.**Statement II** Centre of first circle lie on the second circle.

## Answer

B

**Question**. **Statement I** A ray of light incident at the point (–3, –1) gets reflected from the tangent at (0, –1) to the circle x^{2} + y^{2} = 1. If the reflected ray touches the circle,then equation of the reflected ray is 4 y – 3x = 5.**Statement II** The angle of incidence = angle of reflection i.e., **∠**i = **∠**r

## Answer

B

**Question**. Consider L_{1} 2x + 3y + p – 3 and L2 : 2x + 3y + p + 3 = 0, where pis a real number and C : x^{2} + y^{2} + 6x -10y + 30 = 0

Statement**I** If line L1 is a chord of circle C, then L_{2} is not always a diameter of circle C.**Statement** II If line L1 is a diameter of circleC, then L_{2} is not a chord of circle C . ** **

## Answer

C

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