If P is a point on x² a² + y² b² =1 with focii S and S^ , then the maximum value of S P S^ is

Step-by-step solution

Given equation of an ellipse x² a² + y² b² =1 The area of S P S^ = 1 2 [ array ccc a e & 0 & 1 a & b & 1 -a e & 0 & 1 array ] Expanding w.r, to C₂ aligned &= 1 2 (b )(a e+a e) &=a b e [ -1 1] aligned Here, S^ (-a e, 0) S (a e, 0) Now, maximum value of area aligned &=a b e( maximum value of ) &=a b e(1)=a b e aligned