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The foci of the ellipse $25(x+1)^2+9(y+2)^2=225$ are at
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$(-1,2)$ and $(-1,-6)$
$\begin{aligned} & \frac{(x+1)^2}{\frac{225}{25}}+\frac{(y+2)^2}{\frac{225}{9}}=1 \\ & a=\sqrt{\frac{225}{25}}=\frac{15}{5}, b=\sqrt{\frac{225}{9}}=\frac{15}{3} \Rightarrow e=\sqrt{1-\frac{9}{25}}=\frac{4}{5}\end{aligned}$
Focus $=\left(-1,-2 \pm \frac{15}{3} \cdot \frac{4}{5}\right)=(-1,-2 \pm 4)=(-1,2) ; \quad(-1,-6)$
Focus $=\left(-1,-2 \pm \frac{15}{3} \cdot \frac{4}{5}\right)=(-1,-2 \pm 4)=(-1,2) ; \quad(-1,-6)$
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