The point(s) on the $y-$axis which is (are) at a distance of $13$ units from the point $(-5,7)$, is (are)

The correct options are
A $(0,19)$
C $(0,-5)$
Let $A=(-5,7)$ and $P=(0,y)$ be the required point on the $y$-axis. Then,
$PA=13\Rightarrow P{A}^2=169\Rightarrow (0+5{)}^2+(y-7{)}^2=169\Rightarrow (y-7{)}^2=144\Rightarrow y-7=\pm 12\Rightarrow y=-5,19$

Hence, the required points are $(0,19)$ and $(0,-5)$