How do you convert #x^2 -12y-36=0# to polar form?

1 Answer
Nov 20, 2017

Using #x=rcostheta# and #y=rsintheta#

Explanation:

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Remembering that an x,y coordinate can be represented by a right triangle with angle theta and hypotenuse r, we can derive that #x=rcostheta# and #y=rsintheta#.

Substituting these into your equation leaves the result
#r^2cos^2theta-12rsintheta-36=0#

This is a quadratic expression in r, so use the quadratic formula to solve for r
#r=(12sintheta+-sqrt(12^2sin^2theta+4*36*cos^2theta))/(2cos^2theta)#
#r=(12sintheta+-sqrt(12^2sin^2theta+-12^2cos^2theta))/(2cos^2theta)#
#r=(12sintheta+-12)/(2cos^2theta)#

Therefore,
#r=(6sintheta+-6)/cos^2theta#

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