If equation ( 10 x - 5 ) 2 + ( 10 y - 4 ) 2 = λ 2 ( 3 x + 4 y - 1 ) 2 represents a hyperbola, then

Step-by-step solution

Given, equation of hyperbola is 10 x - 5 2 + 10 y - 4 2 = λ 2 3 x + 4 y - 1 2 can be rewritten as x - 1 2 2 + y - 2 5 2 3 x + 4 y - 1 5 = λ 2 This is of the form of P S P M = e Where, P is any point on the hyperbola and S is a focus and M is the point of directrix. Here, λ 2 > 1 ⇒ λ > 2    ∵ e > 1 ⇒   λ < - 2 or λ > 2