## Intercepting Ellipses

It is possible for two ellipses to intercept in exactly three points. Find two equations that demonstrate this fact. Is it possible for two such ellipses to have the same center?
Source: NCTM Mathematics Teacher

SOLUTION

Vertical ellipse: $25x^2+16y^2-400=0$
Horizontal ellipse: $\left (x-1\right )^2+25y^2-25=0$

If such ellipses are concentric, symmetry will force them to intercept in four points.