Question: Consider the ellipse (x2 / a2) + (y2 / b2) = 1. a. Show that the equation of the ellipse can be written as (xh)2

Consider the ellipse (x2 / a2) + (y2 / b2) = 1.

a. Show that the equation of the ellipse can be written as (xh)2 / a2 + (yk)2 / a2(1 - e2) = 1 Where e is the eccentricity.

b. Use a graphing utility to graph the ellipse (x - 2)2 / 4 + (y - 3)2 / 4(1 - e2) = 1 for e = 0.95, 0.75, 0.5, 0.25, and 0. Make a conjecture about the change in the shape of the ellipse as e approaches 0.

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