Write a polar equation of a conic that has its focus at the origin and satisfies the given conditions.Parabola, directrix $y = - 3$
A) $r = \frac { 3 } { 1 - \sin \theta }$

B) $r = \frac { 3 } { 1 + \sin \theta }$

C) $r= \frac { 1 } { 1 - 3 \cos \theta }$

D) $r = \frac { 3 } { 1 + 3 \cos \theta }$

E) none of these

Question

Write a polar equation of a conic that has its focus at the origin and satisfies the given conditions.Parabola, directrix $y = - 3$
A) $r = \frac { 3 } { 1 - \sin \theta }$

B) $r = \frac { 3 } { 1 + \sin \theta }$

C) $r= \frac { 1 } { 1 - 3 \cos \theta }$

D) $r = \frac { 3 } { 1 + 3 \cos \theta }$

E) none of these

Quizplus · Accepted Answer

The polar equation of a parabola with a directrix parallel to the x-axis and focus at the origin is $r = \frac{ed}{1 - e\sin\theta}$. Since the directrix is $y = -3$, $d = 3$ and $e = 1$ for a parabola, the equation is $r = \frac{3}{1 - \sin\theta}$.

Write a Polar Equation of a Conic That Has Its y=−3y = - 3y=−3

Write a Polar Equation of a Conic That Has Its $y = - 3$