Question

How do you convert `5y=(x+y)^2 -2xy` into a polar equation?

Answer 1

`r=5sintheta`

Explanation:

The relationn between Cartesian or rectangular coordinates `(x,y)` and polar coordinates `(r,theta)` is given by

`x=rcostheta`, `y=rsintheta` and hence `x^2+y^2=r^2`

Therefore we can write `5y=(x+y)^2-2xy` as

`5rsintheta=x^2+y^2+2xy-2xy`

or `5rsintheta=x^2+y^2`

or `5rsintheta=r^2`

or `r=5sintheta`

This is the equation of a circle

graph{5y=(x+y)^2-2xy [-10.13, 9.87, -2.92, 7.08]}