For the following exercises, convert the polar equation of a conic section to a rectangular equation. 3 r =- 2 8 r = 1 + 3 sin 0 r = 2 + 5 cos 0 5 - 3 sin 0 r = 7 3 - 2 cos 0 5 r = 2 r = 2 + 2 sin 0 5 - 11 sin 0 8 - 8 cos 0 6 + 7 cos 0 6sec 0 r(5 + 2 cos 0) = 6 r(2 - cos 0) = 1 r(2.5 - 2.5 sin 0) = 5 r= -2 + 3 sec 0 6csc 0 r= 3 + 2 csc 0 For the following exercises, graph the given conic section. If it is a parabola, label the vertex, focus, and directrix. If it is an ellipse, label the vertices and foci. If it is a hyperbola, label the vertices and foci. 5 2 10 3 2 + cos 0 r = 3 + 3 sin 0 r = 5 - 4 sin 0 1 + 2 cos 0 8 3 4 - 5 cos 0 r= 2 4 - 4 cos 0 r = 1 - sin 0 3 + 2 sin 0 r(1 + cos 0) = 5 r(3 - 4sin 0) = 9 r(3 - 2sin 0) = 6 r(6 - 4cos 0) = 5 For the following exercises, find the polar equation of the conic with focus at the origin and the given eccentricity and directrix. Directrix: x = 4; e = Directrix: x = - 4; e = 5 Directrix: y = 2; e = 2 Directrix: y = - 2; e = 2 Directrix: x = 1; e = 1 Directrix: x = -1; e = 1 1 7 Directrix: x = 2 . 4' Directrix: y = 5' 7 3 2 2 Directrix: y = 4; e = 8 3 Directrix: x = -2; e 3 Directrix: x = -5; e 4 Directrix: y = 2; e = 2.5 W / H Directrix: x = -3; e =