Question

How do you convert `r - 2 cos t = 3 sin t` to rectangular form?

Answer 1

`x^2+y^2-2x-3y=0`

Explanation:

Relation between polar coordinates `(r,t)` and rectangular coordinates is given by `x=rcost`, `y=rsint`, `r^2=x^2+y^2` and `tant=y/x`.

Hence multiplying each term in `r-2cost=3sint` by `r`

`hArrr^2-2rcost=3rsint` or

`x^2+y^2-2x=3y` or

`x^2+y^2-2x-3y=0`

graph{x^2+y^2-2x-3y=0 [-4.313, 5.69, -1.38, 3.62]}