Question

Convert x^2 + y^2 = 8 to a polar equation

Answer 1

r = 8 sin θ is the polar equation

Answer 2

`r=√(8)`

Explanation:

The given equation is
`x^2+y^2=8`

To convert from rectangular coordinates to polar coordinates, we substitute

`x=r\cos(\theta)` and
`y=r\sin(\theta)`.

This implies that;

`(r\cos(\theta))^2+(r\sin(\theta))^2=8`

`(r^2\cos^2(\theta)+r^2\sin^2(\theta)=8`

Factor
`r^2` to get;

`r^2(\cos^2(\theta)+\sin^2(\theta))=8`

Recall that;
`\cos^2(\theta)+\sin^2(\theta)=1`

`\Rightarrow r^2(1)=8`

`\Rightarrow r^2=8`

`\Rightarrow r=√(8)`