Class 11 Mathematics Conic Sections MCQs Set 02

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 the options
Answer: a

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
Answer: b

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
Answer: 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 the options
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: 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)
Answer: d

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 the options
Answer: b

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

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, ∞)
Answer: d

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) T² < 8
d) T² ≤ 8
Answer: d

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 the options
Answer: b

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
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) x²
b) x²=8(y+3)
c) y²=-8(x+3 x²
d) y²=8(x+5) x²
Answer: a

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
Answer: b

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 the options
Answer: c

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
Answer: c

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 the options
Answer: 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 the options
Answer: b

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

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 the options
Answer: 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 options
Answer(a,c)

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
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 x² + y² = 1 satisfies π/2<Θ<π , is
a) (1, 2)
b) (1, 2)
c) (- 2, -1)
d) (- 2, -1) < (1, 2)
Answer: d

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)
Answer: d

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
Answer: a

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)
Answer: d

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 the options
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) x² + y² – 3ax + 2a² – b² = 0
b) (3x² + y² )- 9ax + 8a² – b² = 0
c) x² + y² – 5ax + 6a² – b² = 0
d) x² + y² – ax – b² = 0
Answer: b

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
Answer: a

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 the options
Answer: b

Question: The equation of the circle passing through the points (1,0) and (0, 1) and having the smallest radius is
a) x² + y² +x + y – 2 = 0
b) x² + y² -2x – 2y + 1 = 0
c) x² + y² -x – y = 0
d) x² + y² +2x + 2y + 7 = 0
Answer: c

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
Answer: b

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
Answer: b

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: 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
Answer: 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 the options
Answer: c

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