question_answer

If \[A(-a,0)\] and \[B(a,0)\]are two fixed points, then the locus of the point on which the line AB subtends the right angle, is 

A) \[{{x}^{2}}+{{y}^{2}}=2{{a}^{2}}\]

B) \[{{x}^{2}}-{{y}^{2}}={{a}^{2}}\]

C) \[{{x}^{2}}+{{y}^{2}}+{{a}^{2}}=0\]

D) \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]

Correct Answer: D

Solution :

We know that \[P{{A}^{2}}+P{{B}^{2}}=A{{B}^{2}}\]   \[\Rightarrow \,\,{{(x-a)}^{2}}+{{y}^{2}}+{{(x+a)}^{2}}+{{y}^{2}}={{(2a)}^{2}}\,\] \[\,\Rightarrow \,\,{{x}^{2}}+{{y}^{2}}={{a}^{2}}\].