• question_answer 19) A and B are two fixed points. The locus of a point p such that $\angle \mathbf{APB}$ is a right angle, is A) $2{{x}^{2}}+{{y}^{2}}={{a}^{2}}$        B) ${{x}^{2}}+{{y}^{2}}={{a}^{2}}$    C) ${{x}^{2}}-{{y}^{2}}={{a}^{2}}$                        D) $2{{x}^{2}}-{{y}^{2}}={{a}^{2}}$

[b] $\because$The fixed point A & B will be the extreme point on the diameter of a circle. P be any point on the circle. So, equation of the circle, whose radius is a and centre be the origin be ${{x}^{2}}+{{y}^{2}}={{a}^{2}}$ Hence, option [b] is correct.