Question

How do you find the coordinates of the center, foci, lengths of the major and minor axes given `4x^2+8y^2=32`?

Answer 1

The center is `(0,0)`
The foci are `(2,0)` and `(-2,0)`
Length of major axis is `=2sqrt8`
Length of minor axis is`=4`

Explanation:

`4x^2+8y^2=32`
Dividing by 32, we get
`x^2/8+y^2/4=1`
Comparing this to the equation of the ellipse
`(x-x_0)^2/a^2+(y-y_0^2)/b^2=1`

The center is `(x_0,y_0)=(0,0)`
To determine the foci, we calculate `c=sqrt(a^2-b^2)=sqrt(8-4)=sqrt4=2`
Therefore the foci are `(2,0)` and `(-2,0)`
Length of half the major axis is `a=sqrt8`
and the length of half the minor axis is `b=2`
graph{4x^2+8y^2=32 [-6.244, 6.243, -3.12, 3.123]}