Convert the polar equations to a rectangular equations?!

Question

1058 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-14T08:40:08

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

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

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

$6 r - 3 r sin θ = 4$ $6r-3rsintheta=4$

$r = \sqrt{x^{2} + y^{2}}$ $r=sqrt(x^2+y^2)$
$r sin θ = y$ $rsintheta=y$

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

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

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

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

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

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