Exam 12: Parametric and Polar Curves

Parametric equations and a parameter interval for the motion of a particle in the xy-plane are given. Identify the particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph traced by the particle and the direction of motion. -x = 2 cos t, y = 2 sin t, $\pi$$\le$ t $\le$ 2 $\pi$

Find the vertices and foci of the ellipse. -144 + 49 = 7056

Solve the problem. -Find the foci and asymptotes of the following hyperbola: - = 1

Graph the parabola or ellipse. Include the directrix that corresponds to the focus at the origin. -r =

Graph. - - = 1

Find the area of the specified region. -Shared by the circles r = 3 cos $\theta$ and r = 3 sin $\theta$

Graph. - + 16 = 16

Find the standard-form equation of the hyperbola centered at the origin which satisfies the given conditions. -Asymptotes y = x, y = - x; one vertex is ( 11, 0)

Graph the polar equation. -r = - sin $\theta$