# MCQ Questions For Class 11 Conic Sections with Answers

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 x2 + y2 – 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

B

Question. The centre of a circle is (2, – 3) and the circumference is 10p. Then, the equation of the circle is
(a) x2 + y2 + 4x + 6y +12 = 0
(b) x2 + y2 – 4x + 6y +12 = 0
(c) x2 + y2 – 4x + 6y -12 = 0
(d) x2 + y2 – 4x – 6y -12 = 0

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) y2=8(x+3) x 2
(b) x2=8(y+3)
(c) y2=-8(x+3 x 2
(d) y2=8(x+5) x 2

A

Question: The focus of the parabola y2=4y-4x  is
(a) (0, 2)
(b) (1, 2)
(c) (2, 0)
(d) (2, 1)

A

Question: The equation λx2+4xy+y2+ λx+3y+2=0 parabola, if λ is
(a) -4
(b) 4
(c) 0
(d) None of these

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

B

Question: The latusrectum of the parabola y2=5x+4y+1 is
(a) 5/4
(b) 10
(c) 5
(d) 5/2

A

Question: The equation of parabola having vertex ( , )0 0 , passing through (5 , 2) and symmetric with respect to y-axis is
(a) 3x2=25y
(b) 2x2=25y
(c) 2y2=25x
(d) None of these

B

Question: x -2=t2,y=2t are the parametric equations of the parabola
(a) y2=4x
(b) y2==-4x
(c) x2=-4y
(d) y2==4(x-2)

D

Question: If the point P(4,2)  is one end of the focal chord PQ of the parabola y2=x,  then the slope of the tangent at Q is
(a) -1/4
(b) 1/4
(c) 4
(d) -4

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) y2=12x+6
(b) x2=12y y 2
(c) x2=-12y
(d) y2=-12x+6

C

Question: The tangents and normal at the ends of the latusrectum of a parabola form a
(b) rectangle
(c) square
(d) None of these

C

Question: The locus of the middle points of the focal chords of parabola
y2=4ax  is
(a) y2=a(x-a)
(b) y2=2a(x-a)
(c) y2 =4a(x-a)
(d) None of these

B

Question: If the normal to the parabola y2=4ax at the point P(at2, 2at) cuts the parabola again at Q(aT2,2aT aT), then
(a) – 2≤ T ≤2
(b) T∈(-∞,-8) ∪ (8,∞)
(c) T< 8
(d) T≤ 8

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

A

Question: If tangents at A and B on the parabola y2=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

A

Question: The equation of tangent to the parabola y2=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

C

Question: The tangent to the parabola y2=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

B

Question: If the tangent at the point P(2,) 4 to the parabola y2=8x meets the parabola y2=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

B

Question: At what point on the parabola y2=4x,the normal makes equal angles with the coordinate axes?
(a) (4, 4)
(b) (9, 6)
(c) (4,-4)
(d) (1,-2)

D

Question: The circle x2+y2=5 meets the parabola y2=4x at P and Q . Then, the length PQ is equal to
(a) 2
(b) 2√2
(c) 4
(d) None of these

C

Question: The normal at three points P, Q, R of the parabola y2=4ax  meet in (h k). The centroid of Δ PQR lies on
(a) x = 0
(b) y = 0
(c) x=-a
(d) y=a

B

Question. If the tangent at the point P on the circle x2 + y2 + 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

C

Question. If the abscissae and ordinates of two points P and Q are roots of the equations x2 + 2ax – b2 = 0 and y2 + 2py – q2 = 0 respectively, then the equation of
the circle with PQ as diameter, is
(a) x2 + y2 + 2ax + 2py – b2 – q2 = 0
(b) x2 + y2 – 2ax – 2py + b2 + q2 = 0
(c) x2 + y2 – 2ax – 2py – b2 – q2 = 0
(d) x2 + y2 – 2ax + 2py + b2 + q2 = 0

A

Question. The line 3x – 2y = kmeets the circle x2 + y2 = 4r2 at only one point, if k2 is
(a) 20 r2
(b) 52 r2
(c) 52/9 r2
(d) 20/9 r2

B

Question. A line through (0, 0) cuts the circle x2 + y2– 2ax = 0 at A and B, then locus of the centre of the circle drawn AB as diameter is
(a) x2 + y2 – 2ay = 0
(b) x2 + y2 + ay = 0
(c) x2 + y2 + ax = 0
(d) x2 + y2 – ax = 0

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) (PQ2 . RS2 )/2

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 Θ1 cos Θ2 cosΘ3 = 0
(b) sec Θ1 sec Θ2 secΘ3 = 0
(c) tan Θ1 tan Θ2 tanΘ3 = 0
(d) cot Θ1 cot Θ2 cotΘ3 = 0

A

Question. The range of a, for which the point (a, a) lies inside the region bounded by the curves y = √1 – x2 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

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

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 x2 + y2 – x + 3y = 0 on L1L2 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

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) È (3, ∞)
(b) (-3, 3)
(c) (-∞, 5 2) È (5 2, ∞)
(d) (5 2 – 4, ∞)

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 x2 + y= 1 satisfies π/2<Θ<π , is
(a) (1, 2)
(b) (1, 2)
(c) (- 2, -1)
(d) (- 2, -1) < (1, 2)

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) x2 + y– 3ax + 2a2 – b2 = 0
(b) 3x2 + y)- 9ax + 8a2 – b2 = 0
(c) x2 + y– 5ax + 6a2 – b2 = 0
(d) x2 + y– ax – b2 = 0

B

Question. Equation of chord of the circle x2 + y2 – 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

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

D

Question. Two perpendicular tangents to the circle x2 + y2 = a2 meet at P. Then, the locus of P has the equation
(a) x2 + y2 = 2a2
(b) x2 + y2 = 3a2
(c) x2 + y2 = 4a2
(d) None of these

A

Question. From a point on the circle x2 + y2 = a2, two tangents are drawn to the circle x2 + y2 = a2 sin2α.The angle between them is
(a) α
(b) α/2
(c) 2α
(d) None of these

C

Question. A straight line with slope 2 and y-intercept 5 touches the circle, x2 + y2 + 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)

D

Question. The equation x2 +  y2 + 2gx + 2fy + c = 0 will represent a real circle, if
(a) g2 + f2 – c < 0
(b) g2 + f2 – c ≥ 0
(c) always
(d) None of these

B

Question. The tangents to  x2 +  y2 = a2 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

C

Question. The equation of a line inclined at an angle p/4 to the x-axis, such that the two circles x2 + y= 4, x2 + y2– 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

A

Question. The equation of a circleC1 is x2 + y2 = 4.The locus of the intersection of orthogonal tangents to the circle is the curve C2 and the locus of the intersection of perpendicular tangents to the curve C2 is the curve C3. Then,
(a) C3 is a circle
(b) the area enclosed by the curve C3 is 8p
(c) C2 and C3 are circles with the same centre
(d) None of the above

(a,c)

Question. The equation of the tangents drawn from the origin to the circle x2 + y– 2rx – 2hy + h2 = 0, are
(a) x = 0
(b) y = 0
(c) (h2 – r2 )x – 2rhy = 0
(d) (h2 – r2 )x + 2rhy = 0

(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)

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)

C

Question. If a > 2 b > 0, then the positive value of m for which y = mx – b√(1 + m2) is a common tangent to x2 + y2 = b2 and (x – a)2 + y2 = b2, is

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

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

A

Question. The equation of the circle passing through the points (1,0) and (0, 1) and having the smallest radius is
(a) x2 + y+x + y – 2 = 0
(b) x2 + y-2x – 2y + 1 = 0
(c) x2 + y-x – y = 0
(d) x2 + y+2x + 2y + 7 = 0

C

Question. The point diameterically opposite to the point P(1, 0) on the circle x2 + y+2x + 2y – 3 = 0 is
(a) (3, 4)
(b) (3, – 4)
(c) (- 3, 4)
(d) (- 3, – 4)

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

A

Question. Any chord of the circle x2 + y2 = 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

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) x2 + y=27/4
(b) x2 + y=9/4
(c) x2 + y=3/2
(d)  x2 + y=1

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) x2 + y=2x – 2y – 62 = 0
(b) x2 + y=2x + 2y – 62 = 0
(c) x2 + y=2x + 2y – 47 = 0
(d)x2 + y=2x – 2y – 47 = 0

C

Question. If the pair of lines ax2 + 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) 3a2 + 2ab + 3b2 = 0
(b) 3a2 + 10ab + 3b2 = 0
(c) 3a2 – 2ab + 3b2 = 0
(d) 3a2 – 10ab + 3b2 = 0

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

A

Question. The intercept on the line y = x by the circle x2 + y2 – 2x = 0 is AB. Equation of the circle on ABas a diameter is
(a) x2 + y2 – x – y = 0
(b) x2 + y2 – x + y = 0
(c) x2 + y2 + x + y = 0
(d) x2 + y2 + x – y = 0

A

Question. How many common tangents can be drawn to the following circles x2 + y2 = 6 and x2 + y2 + 6x + 2y + 1 = 0 ?
(a) 4
(b) 3
(c) 2
(d) 1

A

Question. The circle x2 + y2 – 10x – 14 y + 24 = 0 cuts an intercepts on y-axis of length
(a) 5
(b) 10
(c) 1
(d) None of these

B

Question. If the line 3x – 4 y – k = 0, (k > 0) touches the circle x2 + y2 – 4x + 10y + 5 = 0= 0 at (a, b) , then k + a + b is equal to
(a) 20
(b) 22
(c) -30
(d) -28

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

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 x2 + y2 = 4 and x2 + y2 – 8x + 7 = 0 intersect each other at two distinct points.
Statement II Circles with centresC1 andC2 and radii rand r2 intersect at two distinct points, if |C1 C2 |<r1 r2 .

C

Question. Let C1C2 and be two circles with C2 lying inside C1
Statement I
A circle C lying inside C1 touches C1 internally and C2 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.

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.

D

Question. Consider two circles
S ≡ x2 + y2 + 2gx + 2fy = 0
and S’ ≡ x2 + y2 + 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.

B

Question. Statement I Circle x2 + y2 – 6x – 4y + 9 = 0 bisects the circumference of the circle x2 + y2 – 8x – 6y + 23 = 0.
Statement II Centre of first circle lie on the second circle.

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 x2 + y2  = 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