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Find the locus of a point, so that the j...

Find the locus of a point, so that the join of `(-5,1)` and `(3,2)` subtends a right angle at the moving point.

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Lert P(k,h) be a moving point and let `A(-5,1)` and `B(3,2)` be the given points. From the given condition,we have `angle APB=90^@`
Therefore, `DeltaAPB` is a right-angled triangle, Hence,
`AB^2=AP^2+PB^2`
or `(3+5)^2+(2-1)^2=(h+5)^2+(k-1)^2+(h-3)^2+(k-2)^2`
or `65=2(h^2+k^2+2h-3k)+39`
or `h^2+k^2+2h-3k-13=0`
Hence, the locus of `(h,k)` is `x^2+y^2+2x-3y-13=0`.
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