If l₁ and l₂ are the lengths of the perpendiculars drawn from a point on the hyperbola 5 x^2-4 y^2-20=0 to its asymptotes, then l₁^2 l₂^2 100 =

Step-by-step solution

S x^2 4 - y^2 5 =1 It's asymptotes are 5 x-2 y=0 or 5 x+2 y=0 aligned & l₁= | 5 x₀-2 y₀ | 3 and l₂= | 5 x₀+2 y₀ | 3 & l₁ l₂= 5 x₀^2-4 y₀^2 9 = 20 9 l₁^2 l₂^2 100 = 4 81 aligned