Identify the conic and select its correct graph. $r = \frac { 10 } { 2 - \cos \theta }$ A) $\quad e = 2 1 \Rightarrow$ Hyperbola B) $e = \frac { 1 } { 2 } 1 \Rightarrow$ Hyperbola

Question

Identify the conic and select its correct graph. $r = \frac { 10 } { 2 - \cos \theta }$ A) $\quad e = 2 > 1 \Rightarrow$ Hyperbola B) $e = \frac { 1 } { 2 } < 1 \Rightarrow$ Ellipse C) $e = \frac { 1 } { 2 } < 1 \Rightarrow$ Ellipse D) $\quad e = 5 > 1 \Rightarrow$ Hyperbola E) $e = 2 > 1 \Rightarrow$ Hyperbola

Quizplus · Accepted Answer

The given polar equation can be rewritten as $r(2-\cos	heta)=10$. We recognize that this is an ellipse because $0<2-\cos	heta\leq 2$ for all $	heta$, which means that $r$ takes on all nonnegative values. The focus and directrix information is not necessary to determine the conic and its graph. The correct graph for an ellipse is choice (B).

Identify the Conic and Select Its Correct Graph r=102−cos⁡θr = \frac { 10 } { 2 - \cos \theta }r=2−cosθ10​

Identify the Conic and Select Its Correct Graph $r = \frac { 10 } { 2 - \cos \theta }$