If the points P (x, y) is equidistant from A (5, 1) and B (−1, 5), then

It is given that $\mathrm{P}(x, y)$ is equidistant to the point $\mathrm{A}(5,1)$ and $\mathrm{B}(-1,5)$

So,

$\mathrm{PA}^{2}=\mathrm{PB}^{2}$

So apply distance formula to get the co-ordinates of the unknown value as,

$(x-5)^{2}+(y-1)^{2}=(x+1)^{2}+(y-5)^{2}$

On further simplification we get,

$25-10 x+1-2 y=1+2 x+25-10 y$

So,

$12 x=8 y$

Thus,

$3 x=2 y$

So the answer is (c)