Take two cases of the family of curves and generatedOriginally Posted by ling_c_0202
by letting and respectively.
Then find the x-coordinates of the points of intersection of
and (you should find these are and ).
Now substitute these values of back into the RHS of the equation of
and you will find that it is independent of .
So the points corresponding to the values of that you have found are
the same on all the curves (when ).