JEE Advanced2017MathematicsEllipseActual
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
- A(IV) (iii) (S)
- B(II) (iv) (R)
- C(IV) (iv) (S)
- D(II) (iii) (R)
Correct answer
B. (II) (iv) (R)
Step-by-step solution
P 3 , 1 2 ;   tangent 3 x + 2 y = 4 ⇒ 3 x + 4 1 2 y = 4 , comparing with (II) ⇒       a = 2   ∴         y = m x + a 2 m 2 + 1 is tangent for m = - 3 2 i.e. (ii) ∴ Point of contact for a = 2 ,   m = - 3 2 is R