Consider two ellipses in standard position: E1 : x a1 2 + y b1 2 = 1 E2 : x a2 2 + y b2
Chapter 11, Problem 74(choose chapter or problem)
Consider two ellipses in standard position: E1 : x a1 2 + y b1 2 = 1 E2 : x a2 2 + y b2 2 = 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.
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