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!
Hello, 14041471!
Find the Foci of this ellipse: .$\displaystyle \frac{(x-2)^2}{25} + \frac{(y+3)^2}{4} \:=\:1$
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: .$\displaystyle C(2,\text{-}3)$
From $\displaystyle c^2 \:=\:a^2-b^2$, we have: .$\displaystyle c^2 \:=\:25-4 \:=\:21 \quad\Rightarrow\quad c \:=\:\pm\sqrt{21}$
Therefore, the foci are: .$\displaystyle \left(2+\sqrt{21},\:\text{-}3\right)\:\text{ and }\:\left(2-\sqrt{21},\:\text{-}3\right) $