Question

How do you convert `-3y= 2x^2+4xy` into a polar equation?

Answer 1

`r = -3/2(tan theta sec theta)/(1-2 tan theta)`, representing a hyperbola. Graph is inserted.

Explanation:

The conversion formula is (x, y) = r (cos theta, sin theta)#

After conversion,

`-3sin theta = 2rcos theta (cos theta + 2 sin theta)`. Explicitly,

`r=-3/2tan theta/(cos theta+2 sin theta`

`== -3/2(tan theta sec theta)/(1-2 tan theta`.
graph{3y+2x^2+4xy=0 [-5.53, 5.53, -2.765, 2.765]}