Select the polar equation of the conic for e = 0.75 and identify the conic for the following equation. $r = \frac { 2 e } { 1 - e \cos \theta }$
A) $r = \frac { 1.5 } { 1 - 0.75 \cos \theta } \Rightarrow \text { ellipse }$
B) $r = \frac { 1.5 } { 1 - 1.75 \cos \theta } \Rightarrow \text { parabola }$
C) $r = \frac { 0.75 } { 1 + 0.75 \cos \theta } \Rightarrow \text { parabola }$
D) $r = \frac { 1.5 } { 1 + \cos \theta } \Rightarrow \text { ellipse }$
E) $r = \frac { 1.75 } { 1 + \cos \theta } \Rightarrow \text { parabola }$

Question

Select the polar equation of the conic for ​e = 0.75 and identify the conic for the following equation.​ $r = \frac { 2 e } { 1 - e \cos \theta }$ ​
A) $r = \frac { 1.5 } { 1 - 0.75 \cos \theta } \Rightarrow \text { ellipse }$
B) $r = \frac { 1.5 } { 1 - 1.75 \cos \theta } \Rightarrow \text { parabola }$
C) $r = \frac { 0.75 } { 1 + 0.75 \cos \theta } \Rightarrow \text { parabola }$
D) $r = \frac { 1.5 } { 1 + \cos \theta } \Rightarrow \text { ellipse }$
E) $r = \frac { 1.75 } { 1 + \cos \theta } \Rightarrow \text { parabola }$

Quizplus · Accepted Answer

The given equation is $r = \frac { 2 e } { 1 - e \cos \theta }$. Substituting $e = 0.75$, we get $r = \frac { 1.5 } { 1 - 0.75 \cos \theta }$. Since $e = 0.75 < 1$, the conic is an ellipse.

Select the Polar Equation of the Conic for ​E = r=2e1−ecos⁡θr = \frac { 2 e } { 1 - e \cos \theta }r=1−ecosθ2e​

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