How do you convert $r= 1/(6cosθ-2sinθ)$ into cartesian form?

Question

2313 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-21T09:09:13

$6x-2y=1$

for polar co-ordinates

$r^2=x^2+y^2$

$color(red)(x=rcostheta)$

$color(blue)(y=rsintheta)$

for $" "r=1/(6costheta-2sintheta)$

rearrange

$r(6costheta-2sintheta)=1$

$6color(red)(rcostheta)-2color(blue)(rsintheta)=1$

$6color(red)(x)-2color(blue)(y)=1$

How do you convert r= 1/(6cosθ-2sinθ)r= 1/(6cosθ-2sinθ) into cartesian form?