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) $r = \frac { 1 } { 1 + \sin \theta } \Rightarrow \text { parabola }$
B) $r = \frac { 2 } { 1 + \sin \theta } \Rightarrow \text { parabola }$
C) $r = \frac { 2 } { 1 - 2 \sin \theta } \Rightarrow \text { ellipse }$
D) $r = \frac { 2 } { 1 + \sin \theta } \Rightarrow \text { ellipse }$
E) $r = \frac { 2 } { 1 + \sin \theta } \Rightarrow \text { parabola }$.

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) $r = \frac { 1 } { 1 + \sin \theta } \Rightarrow \text { parabola }$
B) $r = \frac { 2 } { 1 + \sin \theta } \Rightarrow \text { parabola }$
C) $r = \frac { 2 } { 1 - 2 \sin \theta } \Rightarrow \text { ellipse }$
D) $r = \frac { 2 } { 1 + \sin \theta } \Rightarrow \text { ellipse }$
E) $r = \frac { 2 } { 1 + \sin \theta } \Rightarrow \text { parabola }$.

Quizplus · Accepted Answer

For e = 1, the conic is a parabola. The equation $r = \frac { 2 } { 1 + \sin \theta }$ matches the form for a parabola with e = 1.

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 = $r = \frac { 2 e } { 1 + e \sin \theta }$