Exam 12: Parametric and Polar Curves

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

Replace the polar equation with an equivalent Cartesian equation. -r = 5 cot $\theta$ csc $\theta$

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 = 3 tan t, y = 4 sec t; - $\pi$ /2 $\le$ t $\le$$\pi$ /2

Graph the polar equation. -r = 3 $\theta$

Graph the pair of parametric equations with the aid of a graphing calculator. -x = t - sin t, y = 1 - cos t, -4 $\pi$ $\le$ t $\le$ 4 $\pi$

Replace the polar equation with an equivalent Cartesian equation. -r = 26 sin $\theta$

Graph. -9 - 25 = 225

Find the standard-form equation of the hyperbola centered at the origin which satisfies the given conditions. -Foci at ( , 0), (- , 0); asymptotes y = 6x, y = -6x

Graph. - - =

Find an equation of the following curve. -An ellipse centered at the origin having vertex at (0, -6) and eccentricity equal to

Graph the pair of parametric equations with the aid of a graphing calculator. -x = cos t + 4 cos 3t, y = 5 cos t - 4 sin 3t, 0 $\le$ t $\le$ 2 $\pi$

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

Graph the pair of parametric equations with the aid of a graphing calculator. -x = 5(t - sin t), y= 5(1 - cos t), 0 $\le$ t $\le$ 4 $\pi$

Find the area of the specified region. -Shared by the circles r = 3 and r = 6 sin $\theta$

Calculate the arc length of the indicated portion of the curve r(t). -r(t) = 3ti + j + k; -8 $\le$ t $\le$ -7

Choose the equation that matches the graph. -

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

Graph. - - = 1

Replace the polar equation with an equivalent Cartesian equation. - sin 2 $\theta$ = 40