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प्रश्न
Find the locus of a point such that the line segments with end points (2, 0) and (−2, 0) subtend a right angle at that point.
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उत्तर
Let the given points be \[A\left( 2, 0 \right)\text{ and }B\left( - 2, 0 \right)\]. Let P(h, k) be a point such that
Thus,
∆ APB is a right angled triangle.
\[\therefore A B^2 = A P^2 + B P^2\]
\[ \Rightarrow 16 = h^2 + 4 - 4h + k^2 + h^2 + 4 + 4h + k^2 \]
\[ \Rightarrow h^2 + k^2 = 4\]
Hence, the locus of (h, k) is x2+ y2 = 4.
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