Today we learned about the polar equations of conics, which includes ellipses, hyperbolas, and parabolas. There are some very important equations you need to do in order to find the polar equations.
- r = ep/ 1+esinθ
- horizontal directrix that is above the pole (positive y)
- r = ep/1-esinθ
- horizontal directrix that is below the pole (negative y)
- r = ep/1+ecosθ
- vertical directrix that is on the right of the pole (positive x)
- r = ep/1-ecosθ
- vertical directrix that is on the left of the pole (negative x)
These are the equations you will use in order to find the conic equation with the given information you are given.
In addition, you must be able to identify an ellipse, parabola, and hyperbola for each conic equation. You can determine this through the eccentricity (e).
ellipse: e< 1
parabola: e= 1
hyperbola: e>1
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