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Question

A(a,0) and B(a,0) are two fixed points. The locus of a point P such that APB is a right angle, is

A
x2+y2=a2
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B
x2y2=a2
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C
x2+y2=2a2
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D
2x2y2=2a2
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Solution

The correct option is A x2+y2=a2
Let P(x,y) be the moving point whose locus is required.
Here, A(a,0) and B(a,0). Given APB=π2
AP2+PB2=AB2


(x+a)2+y2+(xa)2+y2=(2a)2
2x2+2y2+2a2=4a2x2+y2=a2
Which is the required locus.

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