Class 11 Mathematics Conic Sections MCQs Set F

Question: The circle passing through the intersection of the circles, x2 + y2 – 6x = 0 and x2 + y2 – 4y = 0, having its centre on the line, 2x -3y +12 = 0, also passes through the point:
(a) (–1, 3)
(b) (–3, 6)
(c) (–3, 1)
(d) (1, –3)
Answer: b

Question: If one of the diameters of the circle, given by the equation, x² + y² – 4x + 6y – 12 = 0, is a chord of a circle S, whose centre is at (–3, 2), then the radius of S is:
(a) 5
(b) 10
(c) 5√2
(d) 5√3
Answer: d

Question: Equation of the tangent to the circle, at the point (1, –1) whose centre is the point of intersection of the straight lines x – y = 1 and 2x + y = 3 is :
(a) x + 4y + 3 = 0
(b) 3x – y – 4 = 0
(c) x – 3y – 4 = 0
(d) 4x + y – 3 = 0
Answer: a

Question: If a tangent to the circle x² + y² = 1intersects the coordinate axes at distinct points P and Q, then the locus of the midpoint of PQ is:
(a) x² + y² – 4x²y² = 0
(b) x² + y² – 2xy = 0
(c) x² + y² – 16x²y² = 0
(d) x² + y² – 2x²y² = 0
Answer: a

Question: If a variable line, 3x + 4y – λ = 0 is such that the two circles x² + y² – 2x – 2y + 1 = 0 and x² + y² – 18x – 2y + 78 = 0 are on its opposite sides, then the set of all values of λ is the interval :
(a) (2, 17)
(b) [13, 23]
(c) [12, 21]
(d) (23, 31)
Answer: c

Question: The line x = y touches a circle at the point (1, 1). If the circle also passes through the point (1, –3), then its radius is:
(a) 3
(b) 2√2
(c) 2
(d) 3√2
Answer: b

Question: A circle touching the x-axis at (3, 0) and making an intercept of length 8 on the y-axis passes through the point :
(a) (3, 10)
(b) (3, 5)
(c) (2, 3)
(d) (1, 5)
Answer: a

Question: The equation of latusrectum of a parabola is x+ y = 8 and the equation of the tangent at the vertex is x+ y = 12 , then length of the latusrectum is
(a) 4√ 2
(b) 2 √2
(c) 8
(d) 8 √2
Answer: d

Question: The equation of the circle, which touches the line y = 5 and passes through (–1, 2) and (1, 2) is
(a) 9x² + 9y² − 60y + 75 = 0
(b) 9x² + 9y² − 60x − 75 = 0
(c) 9x² + 9y² + 60y − 75 = 0
(d) 9x² + 9y² + 60x + 75 = 0
Answer: a

Question: If the normal at an end of a latus rectum of an ellipse passes through an extermity of the minor axis, then the eccentricity e of the ellipse satisfies:
(a) e⁴ + 2e² – 1 = 0
(b) e² + e – 1 = 0
(c) e⁴ + e2 – 1 = 0
(d) e² + 2e – 1 = 0
Answer: c

Question: If a circle of unit radius is divided into two parts by an arc of another circle subtending an angle 60° on the circumference of the first circle, then the radius of the arc is:
(a) √3
(b) 1/2
(c) 1
(d) None
Answer: d

Question: If the tangent at the point P(2,4) to the parabola y²= 8x +5 at 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: The foci of the ellipse x²/16 + y²/b² = 1 and the hyperbola x²/144 + y²/81= 1/25 coincide. Then the value of b² is
(a) 9
(b) 1
(c) 5
(d) 7
Answer: d

Question: If the circles x² + y² + 2ax + cy + a = 0 and x² + y² – 3ax + dy – 1 = 0 intersect in two distinct points P and Q then the line 5x + by – a = 0 passes through P and Q for
(a) exactly one value of a
(b) no value of a
(c) infinitely many values of a
(d) exactly two values of a
Answer: b

Question: The locus of the mid-point of the line segment joining the focus to a moving point on the parabola y²= 4ax is another parabola with the directrix
(a) x = − a
(b) x=–₂
(c) x = 0
(d) x = a/2 
Answer: c

Question: Point (1, 2) relative to the circle x² + y² + 4x – 2y – 4 = 0 is a/an
(a) exterior point
(b) interior point, but not centre
(c) boundary point
(d) centre
Answer: a

Question: The latusrectum of the parabola y2=4ax whose focal chord is PSQ such that SP = 3 and SQ = 2 , is given by
(a) 24/5
(b) 12/5
(c) 6/5
(d) 1/5 
Answer: d

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

Question: Let C be the circle with centre at (1, 1) and radius = 1. If T is the circle centred at (0, y), passing through origin and touching the circle C externally, then the radius of T is equal to
(a) 1/2
(b) 1/4
(c) √3/√2
(d) √3/2
Answer: b

Question: If the circles x² + y² + 5Kx + 2y + K = 0 and 2 (x² + y²) + 2Kx + 3y – 1= 0, (K∈R), intersect at the points P and Q, then the line 4x + 5y – K = 0 passes through P and Q, for:
(a) infinitely many values of K
(b) no value of K.
(c) exactly two values of K
(d) exactly one value of K
Answer: b

Question: Let the tangents drawn to the circle, x² + y² = 16 from the point P(0, h) meet the x-axis at point A and B. If the area of ΔAPB is minimum, then h is equal to :
(a) 4√2
(b) 3√3
(c) 3√2
(d) 4√3
Answer: a

Question: The length of the latusrectum of the parabola 169 {(x-1)² + (y-3)²} = (5x-12y +17)² is
(a) 14/13
(b) 12/13
(c) 28/13
(d) None of these
Answer: a

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: If the area of an equilateral triangle inscribed in the circle, x² + y² + 10x + 12y + c = 0 is 27√3 sq. units then c is equal to:
(a) 13
(b) 20
(c) – 25
(d) 25
Answer: d

Question: If a focal chord of the parabola y²=ax = is 2x-y-8=0, then the equation of the directrix is
(a) x + = 4 0
(b) x − = 4 0
(c) y − = 4 0
(d) y + = 4 0 
Answer: c

Question: The length of the chord of the parabola x² = 4y passing through the vertex and having slope cot α is
(a) 4 cos α α cosec² α
(b) 4 tan α α sec α
(c) 4 sin α sec² α
(d) None of these 
Answer: a

Question: The angle made by a double ordinate of length 8 a at the vertex of the parabola y²= 4ax is
(a) π/3
(b) π/2
(c) π/4
(d) π/6 
Answer: b

Question: The line x −1 =0 is the directrix of the parabola
y²– kx + 8=0 
(a) 1/8
(b) 8
(c) 4
(d) 1/4 
Answer: c

Question: A circle cuts a chord of length 4a on the x-axis and passes through a point on the y-axis, distant 2b from the origin. Then the locus of the centre of this circle, is
(a) a hyperbola
(b) an ellipse
(c) a straight line
(d) a parabola
Answer: d

Question: If the length of the chord of the circle, x² + y² = r² (r > 0) along the line, y – 2x = 3 is r, then r2 is equal to :
(a) 9/5
(b) 12
(c) 24/5
(d) 12/5
Answer: d

Question: The equation Im [(iz − 2) / (z − i)] + 1 = 0, z ∈C, z ≠ i represents a part of a circle having radius equal to :
(a) 2
(b) 1
(c) 3/4
(d) 1/2
Answer: c

Question: The value of λ does the line y = x + λ touches the ellipse 9x² + 16y² =144 is/are
(a) ± 2√2
(b) 2 ± √3
(c) ± 5
(d) 5 ± √2
Answer: c

Question: The normal at three points P, Q, R of the parabola y²= 4ax meet in ( h,k). The centroid of ΔPQR lies on
(a) x = 0
(b) y = 0
(c) x =-a
(d) y=3 
Answer: 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) 
Answer: d

Question: A rod AB of length 15 cm rests in between two coordinate axes in such a way that the end point A lies on x-axis and end point B lies on y-axis. A point P(x, y) is taken on the rod in such a way that AP = 6 cm. Then, the locus of P is a/an.
(a) circle
(b) ellipse
(c) parabola
(d) hyperbola
Answer: b