# Thread: Converting a polar equation to a rectangular equation

1. ## Converting a polar equation to a rectangular equation

I was given the polar equation: r + 2cos(theta) = 3sin(theta)

Which I converted (I believe correctly) to x^2+y^2=-2x+3y yet my professor circled my answer and circled the word "Equation" in the question. I feel like what I did was right but is there another form I am supposed to put this in? Thank you.

2. ## Re: Converting a polar equation to a rectangular equation

Originally Posted by beastcoast515
I was given the polar equation: r + 2cos(theta) = 3sin(theta)

Which I converted (I believe correctly) to x^2+y^2=-2x+3y yet my professor circled my answer and circled the word "Equation" in the question. I feel like what I did was right but is there another form I am supposed to put this in? Thank you.
\displaystyle \displaystyle \begin{align*} r + 2\cos{(\theta)} &= 3\sin{(\theta)} \\ r + 2\left( \frac{x}{r} \right) &= 3\left( \frac{y}{r} \right) \\ r^2 + 2x &= 3y \\ x^2 + y^2 + 2x &= 3y \\ x^2 + 2x + y^2 - 3y &= 0 \\ x^2 + 2x + 1^2 + y^2 - 3y + \left( -\frac{3}{2} \right)^2 &= 1^2 + \left( -\frac{3}{2} \right)^2 \\ \left( x + 1 \right)^2 + \left( y - \frac{3}{2} \right)^2 &= \frac{13}{4} \\ \left(x + 1 \right)^2 + \left( y - \frac{3}{2} \right)^2 &= \left( \frac{\sqrt{13}}{2} \right)^2 \end{align*}

So this is a circle of radius \displaystyle \displaystyle \begin{align*} \frac{\sqrt{13}}{2} \end{align*} units centred at \displaystyle \displaystyle \begin{align*} \left( -1, \frac{3}{2} \right) \end{align*}.

3. ## Re: Converting a polar equation to a rectangular equation

Yes, that's obviously a circle but the question was, why did the professor circle it and write "equation"? beastcoast515, look closely at your paper again. Is it possible that you simply forgot to write "=" or that you wrote it quickly and it was not easily readable as an equality symbol?
Other than that, if you actually wrote what you say here, I can think of no good reason.

4. ## Re: Converting a polar equation to a rectangular equation

Originally Posted by HallsofIvy
Yes, that's obviously a circle but the question was, why did the professor circle it and write "equation"? beastcoast515, look closely at your paper again. Is it possible that you simply forgot to write "=" or that you wrote it quickly and it was not easily readable as an equality symbol?
Other than that, if you actually wrote what you say here, I can think of no good reason.
Or if the question asked to DESCRIBE the curve given by the equation. There's nearly always an expectation of inference from doing a question...