Find a polar equation of the conic with focus at the pole and the given eccentricity and directrix.

e=3/2,ysinΘ=1

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- Jul 15th 2008, 04:09 PMDave53Can someone explain how I do this one?Find a polar equation of the conic with focus at the pole and the given eccentricity and directrix.

e=3/2,*y*sinΘ=1 - Jul 15th 2008, 07:22 PMTKHunny
There is a rule for eccentricity. e > 1 tells you it is what sort of conic? Hint: You're going to need another focus and directrix.

Conics look like this in polar coordinates: $\displaystyle r = \frac{ep}{1\pm e\sin(\theta)}$ parallel to the polar axis, or

$\displaystyle r = \frac{ep}{1\pm e\cos(\theta)}$ perpendicular to the polar axis.

You have e = 3/2 -- Alarm goes off! This is a hyperbola.

If you mean $\displaystyle r\sin(\theta) = 1$, then we have a horizontal line. (Pretty obvious that this tranlsates to y = 1?). Okay, what form is that?

We are so close...

Note: Is that enough information for uniqueness?