Find a polar equation for the conic described.
-The hyperbola with a focus at the pole and transverse axis endpoints $\left( 4 , \frac { \pi } { 2 } \right)$ and $\left( - 8 , \frac { 3 \pi } { 2 } \right)$
A) $r = \frac { 16 } { 1 + 3 \sin \theta }$
B) $r = \frac { 16 } { 1 - 3 \sin \theta }$
C) $r = \frac { 8 } { 2 + 6 \sin \theta }$
D) $r = \frac { 16 } { 1 + 3 \cos \theta }$

Question

Quizplus · Accepted Answer

The transverse axis is vertical, so the equation has the form $r = \frac { ep } { 1 \pm e \sin \theta }$. The transverse axis length is $4 + 8 = 12$, so $2a = 12$ and $a = 6$. The eccentricity is $e = \frac { c } { a } = \frac { 10 } { 6 } = \frac { 5 } { 3 }$. So, the equation is $r = \frac { 6 ( 5 ) } { 1 \pm \frac { 5 } { 3 } \sin \theta } = \frac { 30 } { 1 \pm \frac { 5 } { 3 } \sin \theta }$.

Find a Polar Equation for the Conic Described (4,π2)\left( 4 , \frac { \pi } { 2 } \right)(4,2π​)

Find a Polar Equation for the Conic Described $\left( 4 , \frac { \pi } { 2 } \right)$