Select the polar equation of the conic for e = 1.0 and identify the conic for the following equation. $r = \frac { 2 e } { 1 - e \sin \theta }$
A) $r = \frac { 2 } { 1 - \sin \theta } \Rightarrow \text { parabola }$
B) $r = \frac { 1 } { 1 + \sin \theta } \Rightarrow \text { hyperbola }$
C) $r = \frac { 2 } { 1 - 2 \sin \theta } \Rightarrow \text { hyperbola }$
D) $r = \frac { 2 } { 1 + \sin \theta } \Rightarrow \text { parabola }$
E) $r = \frac { 2 } { 1 + \sin \theta } \Rightarrow \text { hyperbola }$

Question

Select the polar equation of the conic for e = 1.0 and identify the conic for the following equation.  $r = \frac { 2 e } { 1 - e \sin \theta }$ 
A) $r = \frac { 2 } { 1 - \sin \theta } \Rightarrow \text { parabola }$
B) $r = \frac { 1 } { 1 + \sin \theta } \Rightarrow \text { hyperbola }$
C) $r = \frac { 2 } { 1 - 2 \sin \theta } \Rightarrow \text { hyperbola }$
D) $r = \frac { 2 } { 1 + \sin \theta } \Rightarrow \text { parabola }$
E) $r = \frac { 2 } { 1 + \sin \theta } \Rightarrow \text { hyperbola }$

Quizplus · Accepted Answer

Given $e = 1.0$, substituting $e$ into the equation $r = \frac { 2 e } { 1 - e \sin \theta }$ gives $r = \frac { 2 } { 1 - \sin \theta }$, which is a parabola.

Select the Polar Equation of the Conic for E = r=2e1−esin⁡θr = \frac { 2 e } { 1 - e \sin \theta }r=1−esinθ2e​

Select the Polar Equation of the Conic for E = $r = \frac { 2 e } { 1 - e \sin \theta }$