Match the column:
Column-IColumn-II(i) P, Q lie on the axis and R, S lie on the y-axis. Max…

Question

Match the column:
Column-IColumn-II(i)         P, Q lie on the axis and R, S lie on the y-axis. Maximum number of parabola that can be drawn through these points is[A] 3 (ii) From a point on the    radical axis of Circles S1 ≡ x2 + y2 + 4x – 6y – 12 = 0, S2 ≡ x2 + y2 – 6y – 16 = 0 tangents are drawn to S2. Chord of contact passes through (–25, α2), then [α] can be[B] -3 (iii) If (α, β) be the foot of normal drawn from the point (6, 2) on the parabola y2 = 4x, then roots of equation x2 = β(α – 4) is/are.[C] 2(iv) A variable circle whose centre lie on y2 – 36 = 0 cuts rectangular hyperbola xy = 16 at ,    i = 1, 2, 3, 4 then  can be[D] -2

CGP EDU Academic Team · Accepted Answer

The correct answer is (i) [C]; (ii) [D]; (iii) [C]; (iv) [A]. Ans.
(i) [C]
(ii) [D]
(iii) [C],[D]
(iv) [A],[B]
Sol.
(i) (ax + by + c) (a'x + b'y + c') + λ xy = 0 represents parabola for maximum two values of λ .
(ii) Equation of radical axis is x = – 1. Let P = (–1, β ) ⇒ equation of chord of contact is (x + 3y + 16) – β (y – 3) = 0 ⇒ α 2 = 3
⇒ [ α ] = 1 or – 2
(iii) Equation of normal at ( α, β ) is 2( y – β ) + β (x – α ) = 0 ⇒ β ( α – 4) = 4
(iv)   =

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Column-I	Column-II
(i) P, Q lie on the axis and R, S lie on the y-axis. Maximum number of parabola that can be drawn through these points is	[A] 3
(ii) From a point on the radical axis of Circles S1 ≡ x2 + y2 + 4x – 6y – 12 = 0, S2 ≡ x2 + y2 – 6y – 16 = 0 tangents are drawn to S2. Chord of contact passes through (–25, α2), then [α] can be	[B] -3
(iii) If (α, β) be the foot of normal drawn from the point (6, 2) on the parabola y2 = 4x, then roots of equation x2 = β(α – 4) is/are.	[C] 2
(iv) A variable circle whose centre lie on y2 – 36 = 0 cuts rectangular hyperbola xy = 16 at , i = 1, 2, 3, 4 then can be	[D] -2

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