Exam 10: Parametric Equations and Polar Coordinates

Find the vertex, focus, and directrix of the parabola.

Find the area of the region enclosed by one loop of the curve.

Find an equation for the conic that satisfies the given conditions. ellipse, foci , length of major axis 8

Find the length of the curve. , ,

Find the area that the curve encloses.

Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter.

Write a polar equation in r and of a hyperbola with the focus at the origin, with the eccentricity and directrix .

Find an equation of the ellipse that satisfies the given conditions. Foci: (0, ± 8), vertices (0, ± 9)

Find the equation of the directrix of the conic.

Find .

Graph of the following curve is given. Find its length.

Find an equation of the conic satisfying the given conditions. Hyperbola, foci (5, 6) and (5, -2), asymptotes x = 2y + and x = - 2y +

Write a polar equation of the conic that has a focus at the origin, eccentricity , and directrix . Identify the conic.

If a and b are fixed numbers, find parametric equations for the set of all points P determined as shown in the figure, using the angle ang as the parameter. Write the equations for and .

The exact length of the parametric curve is .

Find an equation of the conic satisfying the given conditions. Hyperbola, foci (5, 6) and (5, -4), asymptotes x = 2y + and x = - 2y +

Find the slope of the tangent line to the given polar curve at the point specified by the value of $\alpha$ .

Find parametric equations for the path of a particle that moves once clockwise along the circle , starting at .

Consider the polar equation . (a) Find the eccentricity and an equation of the directrix of the conic. (b) Identify the conic. (c) Sketch the curve.

Find the vertex, focus, and directrix fo the parabola.