Question

If the normals at (x₁ , y₁ ) . . . . to the hyperbola xy = 2 meet at the point (3, 4), then x₁ , x₂, x₃ , x₄ equals 

(1) 3 

(2) 4 

(3) − 4 

(4) − 3

Answer 1

Correct option (2) 4

Explanation:

⇒ slope of the normal at (α, β) =α²/2.

Equation of the normal at (α, β) is

If the four roots of this equation are x₁ , x₂ , x₃ , x₄ , 

then x₁ x₂ x₃ x₄ = − (− 4) = 4