Distance Formula to Find Condition for Co-Linearity
A −a,0 and B ...
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
x2+ y2 = a2
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B
x2- y2 = a2
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C
2x2+ y2 = a2
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D
pair of lines
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Solution
The correct option is Ax2+ y2 = a2 Let P (x, y) be the moving point whose locus is required. LetA≡(−a,0)andB≡(a,0),Given∠APB=π2∴AP2+PB2=AB2 ⇒(x+a)2+y2+(x−a)2+y2=(2a)2⇒2x2+2y2+2a2=4a2⇒x2+y2=a2
Which is the required locus.
Hence, (a) is the correct answer.