The set of points on the axis of the parabola $2{(x−1)^2+(y−1)^2}=(x+y)^2$ from which three distinct normals can be drawn is the set of points (h,k) lying on the axis of the parabola such that h>3/2?
How to prove this claim?I am not being able to proceed much.Just did some axis rotation to get the form $X^2=4(Y-1)$ (after rotating axes by 45 degrees).
This link is related but does not answer my question completely.