Find a polar equation of the conic with its focus at the pole.
Conics
Vertex or vertices
Parabola $( 10 , \pi / 2 )$
A) $\frac { 20 } { 1 - \sin \theta }$
B) $\frac { 20 } { 1 + \sin \theta }$
C) $\frac { 20 } { 1 - \cos \theta }$
D) $\frac { 20 } { 1 + \cos \theta }$
E) $\frac { - 20 } { 1 - \sin \theta }$

Question

Find a polar equation of the conic with its focus at the pole. ​
Conics
Vertex or vertices
Parabola $( 10 , \pi / 2 )$ ​
A) $\frac { 20 } { 1 - \sin \theta }$
B) $\frac { 20 } { 1 + \sin \theta }$
C) $\frac { 20 } { 1 - \cos \theta }$
D) $\frac { 20 } { 1 + \cos \theta }$
E) $\frac { - 20 } { 1 - \sin \theta }$

Quizplus · Accepted Answer

The polar equation of a conic section with its focus at the pole is given by $r = \frac{ed}{1 \pm e\cos(\theta - \phi)}$ or $r = \frac{ed}{1 \pm e\sin(\theta - \phi)}$, where $e$ is the eccentricity, $d$ is the directrix, and $\phi$ is the angle of orientation. For a parabola, $e = 1$, and since the vertex is at $(10, \pi/2)$, the equation becomes $r = \frac{20}{1 + \sin\theta}$, as the parabola opens upwards along the y-axis (or in the direction of $\theta = \pi/2$).

Find a Polar Equation of the Conic with Its Focus (10,π/2)( 10 , \pi / 2 )(10,π/2)

Find a Polar Equation of the Conic with Its Focus $( 10 , \pi / 2 )$