Question

The point on the y-axis equidistant from $(-5,2)$ and $(9,-2)$ is $(0,-m)$, them $m$

Answer 1

Point on y axis has x-coordinates as $O$

$\therefore$ Let that point be $P(O,y)$

Let $A\equiv (-5,2)$ & $B\equiv (9,-2)$

A.T.Q

$PA=PB$

By distance formula

$\sqrt{(0-(-5{)}^2+(y-2{)}^2)}=\sqrt{(0-9{)}^2+(y-(-2{)}^2)}$

As $PA=PB$

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

$\therefore 25+(y-2{)}^2=81+(y+2{)}^2$

$\therefore 25+y^2-4y+4=81+y^2+4y+4$

$-8y=56$

$y=-7$

According to question

$(0,y)\equiv (0,-m)$

$(0,-7)\equiv (0,-m)$

$\therefore m=7$