Exam 12: Parametric and Polar Curves

Find the standard-form equation of the hyperbola centered at the origin which satisfies the given conditions. -Foci at ( -25, 0), ( 25, 0); asymptotes: y = x, y = - x

Graph the parabola. - = -5y

Graph. -9 - 4 = 36

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

Graph the polar equation. -r = 6 - cos $\theta$

Find the standard-form equation of the ellipse centered at the origin and satisfying the given conditions. -An ellipse with vertices (±7, 0) and foci at (±4, 0)

Graph the polar equation. -r = 8 sin 4 $\theta$

Find the length of the curve. -The spiral r = 3 $\theta$ , 0 $\le$ $\theta$ $\le$$\pi$

Find the vertices and foci of the ellipse. -100 + 9 = 900

Graph the pair of parametric equations with the aid of a graphing calculator. -x = cos 4t, y = sin 3t, 0 $\le$ t $\le$ 2 $\pi$

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

Graph the pair of parametric equations with the aid of a graphing calculator. -x = 6 sin t - sin 6t, y = 6 cos t - cos 6t, 0 $\le$ t $\le$ 2 $\pi$

Graph. - - = 50

Find the area of the specified region. -Inside the outer loop and outside the inner loop of the limacon r = 6 cos $\theta$ - 3

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

Find the focus and directrix of the parabola. - = -12y

Find the vertices and foci of the ellipse. -36 + 100 = 3600

Find the length of the curve. -The parabolic segment r = , 0 $\le$ $\theta$ $\le$

Graph the parabola. - = -3x

Choose the equation that matches the graph. -