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

Question

2541 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-21T05:54:26

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

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]}

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