Question

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

Answer 1

Using `x=rcostheta` and `y=rsintheta`

Explanation:

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`

Hope you enjoyed the ms paint artwork.