Consider two ellipses in standard position:

We say that E₁ is similar to E₂ under scaling if there exists a factor r > 0 such that for all (x, y) on E₁, the point (rx, ry) lies on E₂. Show that E₁ and E₂ are similar under scaling if and only if they have the same eccentricity. Show that any two circles are similar under scaling.

E: E2: 2 y b a1 2 (+) + ( a2 y b = 1 = 1