Consider two ellipses in standard position We say that E 1 is similar to E 2 under scaling if there exists a factor r 0 such that for all (x, y) on E 1 , the point (rx, ry) lies on E 2 Show that E 1 and E 2 are similar under scaling if and only if they have the same eccentricity Show that any two c...

If E and E are similar under scaling then since a 0 and 0 b are points on the first ellipse the s ...

Consider two ellipses in standard position: We say that E 1 is similar to E 2 under

Question:

Consider two ellipses in standard position:

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

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.