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 ： $\frac{(x + 1)^{2}}{36} + \frac{(y - 2)^{2}}{36} = 1$