Consider the points $A = (0, 1)$ and $B = (2, 2)$ in the plane. Find the coordinates of the point $P$ on the $x$-axis such that the segments $AP$ and $BP$ make the same angle with the normal to the $x$-axis at $P$.
I was trying this question but I could not get it, I was using the distance formula, and trying to find out the normal vector to the axis at $P$. But could not able to find it out.
If anybody help me, I would be very thankful to them.