How do you convert $2y= -3x^2+9x$ into a polar equation?

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Answer 1 · 2017-09-19T09:17:59

$r=3sectheta-2/3secthetatantheta$

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

$x=rcostheta$ , $y=rsintheta$ and $x^2+y^2=r^2$

Hence, $2y=-3x^2+9x$ can be written as

$2rsintheta=-3r^2cos^2theta+9rcostheta$

or $2sintheta=-3rcos^2theta+9costheta$

or $3rcos^2theta=9costheta-2sintheta$

or $r=(9costheta)/(3cos^2theta)-(2sintheta)/(3cos^2theta)$

or $r=3sectheta-2/3secthetatantheta$

How do you convert 2y= -3x^2+9x 2y= -3x^2+9x into a polar equation?