Writing an Equation in Cartesian Coordinates?

**kellylanemccann** · February 15th 2010, 10:57 PM

How do I write an equation in Cartesian coordinates for the points in the plane that satisfy...
p^2 + psinø = 2cosø
My guess is...
p^2 + py = 2x^2
Am I on the right track?

**Prove It** · February 15th 2010, 11:22 PM

Originally Posted by kellylanemccann

How do I write an equation in Cartesian coordinates for the points in the plane that satisfy...
p^2 + psinø = 2cosø
My guess is...
p^2 + py = 2x^2
Am I on the right track?

Since $x = r\cos{\theta}$ and $y = r\sin{\theta}$

$\cos{\theta} = \frac{x}{r}$ and $\sin{\theta} = \frac{y}{r}$ .

So $p^2 + p\sin{\theta} = 2\cos{\theta}$

$p^2 + p\left(\frac{y}{r}\right) = 2\left(\frac{x}{r}\right)$

$p^2 + \frac{py}{r} = \frac{2x}{r}$

$\frac{py}{r} = \frac{2x}{r} - p^2$

$py = 2x - p^2r$

$y = \frac{2x}{p} - pr$ .

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