Question

Find an equation equivalent to x2 - y2 = 4 in polar coordinates.

Answer 1

The answer is D r^2 cos2(theta) = 4

Explanation:

The person above me simplified it too much.

Answer 2

`r^2=4\sec 2\theta}`

Explanation:

The given equation is:

`x^2-y^2=4`

We substitute
`x=r\cos (\theta)` and
`y=r\sin (\theta)` to obtain:

`r^2\cos^2\theta-r^2\sin^2\theta=4`

This implies that:

`r^2(\cos^2\theta-\sin^2\theta)=4`

Apply double angle identity to obtain:

`r^2\cos 2\theta=4`

This implies that:

`r^2=(4)/(\cos 2\theta)`

This simplifies to:

`r^2=4\sec 2\theta}`