SOLUTION: Write an equation for the ellipse with vertices (2,2),(4,2),(3,-1), and (3,5).

Plot the points:



Sketch the ellipse:



It's shaped like the number zero 0, so it has equation:



Draw the major and minor axes:



The ases cross at the center, which is (h,k) = (3,2)

Counting the units, we see that the major axis is 6, and the semi-major
axis is a = 3, half of 6.

Counting the units, we see that the minor axis is 2, and the semi-minor
axis is b = 1, half of 1.

So we substitute, h=3, k=2, a=3, and b=1 in



and get





Edwin