Find a polar equation for the conic section with focus and the given directrix and eccentricity. Directrix

Question

Find a polar equation for the conic section with focus  and the given directrix and eccentricity. Directrix

Quizplus · Accepted Answer

The polar equation for a conic section with focus $F$ and directrix $r=d/(1+e\cos	heta)$ is given by $r=\dfrac{d}{1+e\cos(	heta-	heta_0)}$ where $	heta_0$ is the angle between the polar axis and the line connecting the focus to the pole. In this case, $d=11eaa88b_9407_05c3_a696_15db2bdc3330_TB5869_11$ and $e=\dfrac{PF}{d}=1$, since the eccentricity is equal to 1 for a parabola. The directrix is vertical, so the angle between the polar axis and the line connecting the focus to the pole is $	heta_0=\pi/2$. Substituting these values into the formula gives $r=\dfrac{11eaa88b_9407_05c3_a696_15db2bdc3330_TB5869_11}{1+\cos(	heta-\pi/2)}=\boxed{	extbf{(C)}\ 11eaa88b_9407_53e7_a696_af86da00c0a6_TB5869_11}$.

Find a Polar Equation for the Conic Section with Focus