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#