Question

Find a point on y-axis which is equidistant from the points $(5,-2)$ and $(-3,2)$.

Answer 1

Let $P(0,y)$ be any point on y-axis. and $A(5,-2)$ and $B(-3,2)$. Then,

$\therefore PA=PB$ (Given)

$\Rightarrow P{A}^2=P{B}^2$

$\Rightarrow (5-0{)}^2+(-2-y{)}^2=(-3-0{)}^2+(2-y{)}^2$

$\Rightarrow 25+4+4y+y^2=9+4+y^2-4y$

$\Rightarrow 8y=-16$

$\Rightarrow y=-2$

Hence, the required point is $(0,-2)$