Question

Given the points $A(5,-3)$ and $B(-1,-5)$. Find the equation of the locus of the point $P$ such that segment $AB$ subtends a right angle at $P$.

Answer 1

Solution -

$A(5,-3)$

$B(-1,-5)$

Locus of P will be a circle whose

diametric end points are A and B.

centre $\to (\frac{5-1}{2},\frac{-3-5}{2})=(2,-4)$

Radius $=\sqrt{(5-2{)}^2+(-3+4{)}^2}=\sqrt{10}$

Locus of $P-$

$(x-2{)}^2+(y+4{)}^2=(\sqrt{10}{)}^2$

$(x-2{)}^2+(y+4{)}^2=10$.