Find the equation of the ellipse that has \( (-3,2),(5,2),(1,-4) \), and \( (1,8) \) for the ends of its axes.
\[
\frac{(x-[?])^{2}}{[]}+\frac{(y-[])^{2}}{[]}=1
\]
Answer
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Answer
\[\frac{(x+1)^2}{36}+\frac{(y-2)^2}{36}=1\]
Steps
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 ：\[\frac{(x+1)^2}{36}+\frac{(y-2)^2}{36}=1\]
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