Foci of Ellipse, urgent help needed

**14041471** · January 18th 2009, 07:01 AM

I need to find the Foci of this Ellipse in standard form:
(1/25)(x - 2)^2 + (1/4)(y + 3)^2 = 1 .

please help!

**Soroban** · January 18th 2009, 07:12 AM

Hello, 14041471!

Find the Foci of this ellipse: . $\frac{(x-2)^2}{25} + \frac{(y+3)^2}{4} \:=\:1$

We see that this is a "horizontal" ellipse.
The major axis is horizontal; the foci are to the right and left of the center.

We see that the center is: . $C(2,\text{-}3)$

From $c^2 \:=\:a^2-b^2$ , we have: . $c^2 \:=\:25-4 \:=\:21 \quad\Rightarrow\quad c \:=\:\pm\sqrt{21}$

Therefore, the foci are: . $\left(2+\sqrt{21},\:\text{-}3\right)\:\text{ and }\:\left(2-\sqrt{21},\:\text{-}3\right)$

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