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JEE Advanced2017MathematicsParabolaActual

Columns 1, 2 and 3 contain conics, equations of tangents to the conics and points of contact, respectively. Column 1 Column 2 Column 3 (I) x 2 + y 2 = a 2 (i) m y = m 2 x + a (P) a m 2 , 2 a m (II) x 2 + a 2 y 2 = a 2 (ii) y = m x + a m 2 + 1 (Q) - m a m 2 + 1 , a m 2 + 1 (III) y 2 = 4 a x (iii) y = m x + a 2 m 2 - 1 (R) - a 2 m a 2 m 2 + 1 , 1 a 2 m 2 + 1 (IV) x 2 - a 2 y 2 = a 2 (iv) y = m x + a 2 m 2 + 1 (S) - a 2

Options

  1. A(III) (i) (P)
  2. B(II) (iv) (R)
  3. C(III) (ii) (Q)
  4. D(I) (ii) (Q)

Correct answer

A. (III) (i) (P)

Step-by-step solution

y = x + 8 is tangent ⇒    m = 1 ; P 8 , 16 Comparing tangent with (i) of column- 2 , m = 1 satisfied and a = 8 is obtained which matches for point of contact (P) of column 3 and (III) of column- I.

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