Class 11 Mathematics Conic Sections MCQs Set H

Question: If the equation of parabola is x² = -9y, then equation of directrix and length of latusrectum are
(a) y = −9/4,8
(b) x =9/4,9
(c) y = 9/4,9 
(d) None of these 
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) y² = 8(x+3)
(b) x2 = 8(y+3)
(c) y2 = -8(8+3)
(d) y2 = 8(x+5) 
Answer: a

Question: The parametric coordinates of any point on the parabola y² = 4ax can be
(a) ( a-at²,-2at 
(b) (a− at²,2at)
(c) (a sin² t,-2a sin t) 
(d) (a sint,-2 a cot) 
Answer: c

Question: A circle touches the y-axis at the point (0, 4) and passes through the point (2, 0). Which of the following lines is not a tangent to this circle?
(a) 4x – 3y + 17 = 0
(b) 3x – 4y – 24 = 0
(c) 3x + 4y – 6 = 0
(d) 4x + 3y – 8 = 0
Answer: d

Question: If a circle passing through the point (–1, 0) touches y-axis at (0, 2), then the length of the chord of the circle along the x-axis is :
(a) 3/2
(b) 3
(c) 5/2
(d) 5
Answer: b

Question: The equation (X-2)² + (Y-3)²=(3X+4Y-2/5)² represents
(a) a parabola
(b) a pair of straight lines
(c) an ellipse
(d) a hyperbola 
Answer: a

Question: A line drawn through the point P(4, 7) cuts the circle x² + y² = 9 at the points A and B. Then PA·PB is equal to :
(a) 53
(b) 56
(c) 74
(d) 65
Answer: b

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

Question: The equation of tangent to the parabola y²=9x which goes through the 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 y²=4ax at the point(a,2a) makes with x-axis an angle equal to
(a) π/3
(b) p/4
(c) p/2
(d) p/6 
Answer: b

Question: Two circles with equal radii are intersecting at the points (0, 1) and (0, –1). The tangent at the point (0, 1) to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is :
(a) 1
(b) 2
(c) 2√2
(d) √2
Answer: d

Question: The equation represents λX²+4XY+Y²+λx+3Y+2=0 represents a parabola, if λis
(a) -4
(b) 4
(c) 0
(d) None of these 
Answer: b

Question: Two sets A and B are as under :
A = {(a, b) ∈R × R : | a -5| <1 and | b – 5 | < 1};
B = {(a,b) ∈R × R : 4(a- 6)² + 9(b- 5)² ≤ 36}. Then :
(a) A ⊂ B
(b) A ∩ B = Φ (an empty set)
(c) neither A ⊂ B nor B ⊂ A
(d) B ⊂ A
Answer: a

Question: If the curves, x² – 6x + y² + 8 = 0 and x² – 8y + y² + 16 – k = 0, (k > 0) touch each other at a point, then the largest value of k is ______.
Answer: 36

Question: The number of integral values of k for which the line, 3x + 4y = k intersects the circle, x² + y² – 2x – 4y + 4 = 0 at two distinct points is ________.
Answer: 9

ASSERTION- REASON TYPE QUESTIONS

(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion:
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

Question: Assertion : Centre of the circle x² + y² – 6x + 4y – 12 = 0 is (3, –2).
Reason : The coordinates of the centre of the circle x² + y² + 2gx + 2fy + c = 0 are (–1/2 coefficient of x, – 1/2 coefficient of y)
Answer: a

Question: Assertion : Latus rectum of a parabola is a line segment perpendicular to the axis of the parabola, through the focus and whose end points lie on the parabola.
Reason : The equation of a hyperbola with foci on the y-axis is : x²/a² − y²/b²= 1
Answer: c

Question: Assertion : Ellipse x²/25 + y²/16= 1 and 12x² – 4y² = 27 intersect each other at right angle.
Reason : Whenever focal conics intersect, they intersect each other orthogonally.
Answer: a

Question: Parabola is symmetric with respect to the axis of the parabola.
Assertion: If the equation has a term y² , then the axis of symmetry is along the x-axis.
Reason: If the eqution has a term x², then the axis of symmetry is along the x-axis.
Answer: c