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Question

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

A
+ =
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B
- =
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C
+ =
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D
None of these
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Solution

The correct option is A + =
Let P (x, y) be the moving point whose locus is required. LetA(a,0)andB(a,0),GivenAPB=π2AP2+PB2=AB2

(x+a)2+y2+(xa)2+y2=(2a)22x2+2y2+2a2=4a2x2+y2=a2
Which is the required locus.
Hence, (a) is the correct answer.

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