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

Question

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

Quizplus · Accepted Answer

Given $e = 1.0$, substituting $e$ into the equation $r = \frac { 2 e } { 1 + e \cos \theta }$ gives $r = \frac { 2 } { 1 + \cos \theta }$. For conic sections, an eccentricity ($e$) of 1 indicates a parabola.

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