Problem
Find the equation of the ellipse that has \( (-3,2),(5,2),(1,-4) \), and \( (1,8) \) for the ends of its axes. \[ \frac{(x-[?])^{2}}{[]}+\frac{(y-[])^{2}}{[]}=1 \]
Solution
Step 1 ：\[\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1\]
Step 2 ：h=-1, k=2, a=6, b=6
Step 3 ：\[\frac{(x+1)^2}{36}+\frac{(y-2)^2}{36}=1\]
