Question

A line parallel to the straight line 2x – y = 0 is tangent to the hyperbola \(\frac{x^2}{4}-\frac{y^2}{2}= 1\) at the point (x₁ , y₁). Then x²₁ + 5y₁² + is equal to :  

(1) 5 

(2) 6 

(3) 8 

(4) 10

Answer 1

Answer is (2) 6

Slope of tangent is 2, Tangent of hyperbola 

\(\frac{x^2}{4}-\frac{y^2}{2}= 1\) at the point (x₁ , y₁) is

(x₁ , y₁) lies on hyperbola