The area of the triangle formed by the tangent to the curve x y= a ^2 at (x₁, y₁ ) on it and the axes is

Step-by-step solution

let Point P be (a t, a t ) aligned & x y=a^2 & eqn of tangent at P : aligned t y+ x t -2 a=0 When y=0 : x = 2 a tA(2 a t, 0) When x=0y= 2 a t B (0, 2 a t ) . A B O if a right ar ( A B O)= 1 2 2 a t 2 a t=2 a^2