Question

Find the 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.

Let $A(5,-2)$ and $B(-3,2)$. Then,

$PA=PB$

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

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

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

$8y=-16$

$y=-2$

Therefore, the required point is $(0,-2)$.