#### Question

Given M and N are fixed points on y axis with coordinates (0,1), (0,-1). Point P is a dynamic point on parabola y = \dfrac{1}{4}x^2

Evaluate position relationship between the line y=-1 and the circle that is centered at P with radius PM.

Let point Q is the intersecting point of the line PM with the parabola y = \dfrac{1}{4}x^2 on another side. Show that \angle PNM = \angle QNM