# How do you find the coordinates of the center, foci, lengths of the major and minor axes given y^2/18+x^2/9=1?

Nov 11, 2016

The center is $= \left(0 , 0\right)$
The lengh of the major axis is $= 6 \sqrt{2}$
The length of the minor axis is $= 6$

#### Explanation:

The general equation of the ellipse is
${\left(y - h\right)}^{2} / {a}^{2} + {\left(x - k\right)}^{2} / {b}^{2} = 1$
The center is $= \left(k , h\right)$

The foci are $\left(k , h \pm c\right)$

The center is $= \left(0 , 0\right)$
The lengh of the major axis is $= 2 \cdot \sqrt{18} = 6 \sqrt{2}$
The length of the minor axis is $= 2 \sqrt{9} = 6$
To determine the foci, we need $c = \sqrt{18 - 9} = 3$
Therefore, the foci are F$= \left(0 , 3\right)$ and F'$\left(0 , - 3\right)$

graph{(y^2/18)+(x^2/9)=1 [-11.25, 11.25, -5.625, 5.625]}