Question

The point(s) on $y-$ axis which is equidistant from the points $(12,3)$ and $(-5,10)$ is/are

• A. $(0,-4)$
• B. $(0,4)$
• C. $(0,2)$
• D. $(0,-2)$

Answer 1

The correct option is D $(0,-2)$

Let a point on $y-$ axis be $(0,k)$,
$\sqrt{(12-0{)}^2+(3-k{)}^2}=\sqrt{(-5-0{)}^2+(10-k{)}^2}$
Squaring both sides,
$\Rightarrow 144+9+k^2-6k=25+100+k^2-20k$
$\Rightarrow 14k=-28$
$\Rightarrow k=-2$

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