How do you convert $y^2 =9x$ to polar form?

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Answer 1 · 2018-04-01T00:11:46

$r=9cotthetacsctheta$

The conversion from Rectangular to Polar:
$x=rcostheta$
$y=rsintheta$

Substitute for $x$ and $y$ :
$(rsintheta)^2=9(rcostheta)$
$r^2sin^2theta=9rcostheta$
$r^2sin^2theta-9rcostheta=0$
$r(rsin^2theta-9costheta)=0$

At this point either $r=0$ or $rsin^2theta-9costheta=0$ , let's solve the second one to get a meaningful answer:

$rsin^2theta=9costheta$

$r=(9costheta)/sin^2theta$

$r= (9costheta)/sintheta*1/sintheta$

Remember: $costheta/sintheta=cottheta$ and $1/sintheta= csctheta$ :

$r=9cotthetacsctheta$

How do you convert y^2 =9xy^2 =9x to polar form?