In a A B C with fixed base B C , the vertex A moves such that B+ C=4 ^2 A 2 . If a, b and c denote the lengths of the sides of the triangle opposite to the angles A, B and C respectively, then

Step-by-step solution

Given, B+ C=4 ^2 A 2 aligned & 2 ( B+C 2 ) ( B-C 2 )=4 ^2 A 2 & 2 A 2 [ ( B-C 2 )-2 A 2 ]=0 & ( B-C 2 )-2 ( B+C 2 )=0 & - B 2 C 2 +3 B 2 C 2 =0 & B 2 C 2 = 1 3 & (s-a)(s-c) s(s-b) (s-b)(s-a) s(s-c) = 1 3 & s-a s = 1 3 2 s=3 a & b+c=2 a aligned Locus of A is an ellipse.