Question

How do you convert `x - y= 4` into polar form?

Answer 1

`r = 4/(cos(theta)-sin(theta))`

Explanation:

When converting between rectangular and polar, we use the following:

`{(x = rcos(theta)), (y = rsin(theta)):}`

(see How do you convert rectangular coordinates to polar coordinates? for an explanation as to why this works)

Then, substituting these in, we get

`x - y = 4`
`=> rcos(theta) - rsin(theta) = 4`
`=> r(cos(theta)-sin(theta)) = 4`
`=> r = 4/(cos(theta)-sin(theta))`