From a point P , tangents are drawn to the curve x 2 2 - y 2 = 1 . If the chord of contact is a normal chord and the locus of P is the curve 8 x 2 - 1 y 2 = 10 λ , then the value of λ is equal to

Step-by-step solution

Let P h , k , then equation of chord of contact is h x 2 - k y = 1 … … i And equation of normal to hyperbola is 2 x cos ⁡ ϕ + y cot ⁡ ϕ = 3 … … i i On comparing i and i i , we get, cot ⁡ ϕ = - 3 k ,   sec ⁡ ϕ = 2 2 3 h Now eliminating ϕ , we get, 8 h 2 - 1 k 2 = 9 ∴ λ = 0.9