A polar equation of a conic is given.
$r = \frac{15}{4 + 3\cos(\theta)}$
(a) Graph the ellipse.
(b) Find the vertices (in polar coordinates with $r > 0$ and $0 \le \theta < 2\pi$) and directrix (as an equation in rectangular coordinates).
vertex (closest to origin) $(r, \theta) = (\frac{15}{7}, 0)$
vertex (farthest from origin) $(r, \theta) = (15, \pi)$
directrix $x = 5$
(c) Find the center of the ellipse (in polar coordinates with $r > 0$ and $0 \le \theta < 2\pi$) and the lengths of the major and minor axes.
center $(r, \theta) = (\frac{60}{7}, \pi)$
length of major axis 17
length of minor axis 17
