Question

If 2x + √6y = 2 touches the hyperbola x² - 2y² = 4 , then the point of contact is

(a)  (1/2,1/√6)

(b)  (4, - √6)

(c)  (4, √6)

(d)  (-2, √6)

Answer 1

Correct option  (b)  (4, - √6)

Explanation :

Suppose 2x +  √6y = 2 touches at (x₁, y₁). At (x₁, y₁), the equation of the tangent to the hyperbola is

xx₁/4  - yy₁/2 = 1

That is, both equations represent the tangent at (x₁,y₁) . Hence

Hence point of contact = (4, - √6)