Change the following polar equation to rectangular form.r=cotΘFind a polar equation of the conic with focus at the pole and the given eccentricity and directrix.e=3/2,ysinΘ=1Thanks again for the help!Dave

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- Jul 14th 2008, 05:07 PMDave53Can someone help me with these two?Change the following polar equation to rectangular form.r=cotΘFind a polar equation of the conic with focus at the pole and the given eccentricity and directrix.e=3/2,
*y*sinΘ=1Thanks again for the help!Dave - Jul 14th 2008, 05:43 PMtopsquark
$\displaystyle r = cot(\theta)$

$\displaystyle r = \frac{cos(\theta)}{sin(\theta)}$

$\displaystyle r~sin(\theta) = cos(\theta)$

Now,

$\displaystyle y = r~sin(\theta)$

and

$\displaystyle x = r~cos(\theta) \implies cos(\theta) = \frac{x}{r} = \frac{x}{\sqrt{x^2 + y^2}}$

So

$\displaystyle y = \frac{x}{\sqrt{x^2 + y^2}}$

-Dan