$\text { The graph of the polar equation }$ $r=\frac{3}{4-3 \cos \theta}$
A) $\text { circle }$
B) $\text { ellipse }$
C) $\text { hyperbola }$
D) $\text { parabola opening up or down }$
E) $\text { parabola opening right or left }$

Question

$\text { The graph of the polar equation }$  $r=\frac{3}{4-3 \cos \theta}$
A) $\text { circle }$
B) $\text { ellipse }$
C) $\text { hyperbola }$
D) $\text { parabola opening up or down }$
E) $\text { parabola opening right or left }$

Quizplus · Accepted Answer

The given polar equation is of the form $r = \frac{e}{1 - e \cos \theta}$, which represents a conic section with the directrix perpendicular to the initial line (polar axis). The value of $e$ (eccentricity) determines the type of conic. Since $e < 1$ (in this case, $e = 3/4$), the conic is an ellipse.

The graph of the polar equation \text { The graph of the polar equation } The graph of the polar equation r=34−3cos⁡θr=\frac{3}{4-3 \cos \theta}r=4−3cosθ3​

$\text { The graph of the polar equation }$ $r=\frac{3}{4-3 \cos \theta}$