Conic Sections in Polar Coordinates
1 Define Conics in Terms of a Focus and a Directrix
-$$r = \frac { 5 } { 4 + 2 \cos \theta }$$
A) ellipse; The directrix is $\frac { 5 } { 2 }$ unit(s) to the right of the pole at $x = \frac { 5 } { 2 }$.
B) ellipse; The directrix is $\frac { 5 } { 2 }$ unit(s) to the left of the pole at $x = - \frac { 5 } { 2 }$.
C) ellipse; The directrix is $\frac { 5 } { 2 }$ unit(s) below the pole at $y = - \frac { 5 } { 2 }$.
D) ellipse; The directrix is $\frac { 5 } { 2 }$ unit(s) above the pole at $y = \frac { 5 } { 2 }$.

Question

Quizplus · Accepted Answer

The given equation is in the form $ r = \frac{ed}{1 + e \cos \theta} $, where $ e = \frac{1}{2} $ (less than 1, indicating an ellipse) and $ d = \frac{5}{2} $. The directrix is to the right of the pole at $ x = \frac{5}{2} $.

Conic Sections in Polar Coordinates 1 Define Conics in Terms r=54+2cos⁡θr = \frac { 5 } { 4 + 2 \cos \theta }r=4+2cosθ5​

Conic Sections in Polar Coordinates
1 Define Conics in Terms $r = \frac { 5 } { 4 + 2 \cos \theta }$