Convert the polar equations to a rectangular equations?!

Question

1055 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-14T08:40:08

C. $36x^2+27y^2-24y-16=0$

Multiply both sides by $6csctheta-3$ to get:
$r(6csctheta-3)=4csctheta$

Then multiply each side by $sintheta$ to cancel out the $csctheta$

$6r-3rsintheta=4$

$r=sqrt(x^2+y^2)$
$rsintheta=y$

$6sqrt(x^2+y^2)-3y=4$

$6sqrt(x^2+y^2)=4+3y$

$36(x^2+y^2)=(4+3y)^2$

$36x^2+36y^2=16+24y+9y^2$

$36x^2+36y^2-16-24y-9y^2=0$

$36x^2+27y^2-24y-16=0$ which is the same as C