Consider the polar equation: $r = \frac { 8 } { 1 - 0.4 \cos \theta }$ Identify the conic without graphing the equation.

A) $e

Question

Consider the polar equation:​ $r = \frac { 8 } { 1 - 0.4 \cos \theta }$ ​ Identify the conic without graphing the equation.
​
A) $e < 1$ ,the conic is a parabola.
B) $e < 1$ ,the conic is a circle.
C) $e < 1$ ,the conic is a hyperbola.
D) $e < 1$ ,the conic is an ellipse.
E)None of the above

Quizplus · Accepted Answer

The polar equation of a conic section is given by $r = \frac { l } { 1 - e \cos \theta }$ where $e$ is the eccentricity. If $0 \leq e < 1$, the conic is an ellipse. In the given equation, $e = 0.4$, which is less than 1, indicating that the conic is an ellipse.

Consider the Polar Equation:​ r=81−0.4cos⁡θr = \frac { 8 } { 1 - 0.4 \cos \theta }r=1−0.4cosθ8​

Consider the Polar Equation: $r = \frac { 8 } { 1 - 0.4 \cos \theta }$