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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