How do you convert $2y= 7x^2-2x$ into a polar equation?

Question

1471 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-01T17:16:08

$r=(2(sintheta+costheta))/(7cos^2theta)$

The relation between polar coordinates $(r,theta)$ and Cartesian coordinates $(x,y)$ is given by

$x=rcostheta$ and $y=rsintheta$

Hence $2y=7x^2-2x$ van be written as

$2rsintheta=7(rcostheta)^2-2rcostheta$

or $2rsintheta+2rcostheta=7r^2cos^2theta$

or $2r(sintheta+costheta)=7r^2cos^2theta$

or $r=(2(sintheta+costheta))/(7cos^2theta)$

How do you convert 2y= 7x^2-2x 2y= 7x^2-2x into a polar equation?