Question

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`?

Answer 1

The center is `=(0,0)`
The lengh of the major axis is `=6sqrt2`
The length of the minor axis is `=6`

Explanation:

The general equation of the ellipse is
`(y-h)^2/a^2+(x-k)^2/b^2=1`
The center is `=(k,h)`

The foci are `(k,h+-c)`

The center is `=(0,0)`
The lengh of the major axis is `=2*sqrt18=6sqrt2`
The length of the minor axis is `=2sqrt9=6`
To determine the foci, we need `c=sqrt(18-9)=3`
Therefore, the foci are F`=(0,3)` and F'`(0,-3)`

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