VITEEE 2013 Paper

Solving the equation of line and curve, we get
x2 - 2 {

2−2x

√6

}2 = 4
⇒ x2−

1

3

× 4 (1 + x2 - 2x) = 4
⇒ 3x2 - 4 - 4x2 + 8x = 12
⇒ x2 - 8x + 16 = 0
⇒ (x−4)2 = 0 ⇒ x = 4
and √6 y = 2 - 2 (4) = - 6
⇒ y = - √6
∴ Point of contact is (4 , - √6)