Exam 10: Parametric Equations and Polar Coordinates

Find the length of the curve.Select the correct Answer

Select the correct Answer: for each question -Find parametric equations to represent the line segment from

Select the correct Answer: for each question. -The orbit of Hale-Bopp comet, discovered in 1995, is an ellipse with eccentricity and one focus at the Sun.The length of its major axis is AU.[An astronomical unit (AU) is the mean distance between Earth and the Sun, about 93 million miles.] Find the maximum distance from the comet to the Sun.(The perihelion distance from a planet to the Sun is and the aphelion distance is ) Find theAnswer in AU and round to the nearest hundredth.

Select the correct Answer: for each question. -Write a polar equation of the conic that has a focus at the origin, eccentricity and directrix Identify the conic.

Find an equation of the hyperbola with vertices and asymptotes

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

Find an equation of the parabola with focus and directrix

Select the correct Answer: for each question -Find a polar equation for the curve represented by the given Cartesian equation.

Write a polar equation in and of an ellipse with the focus at the origin, with the eccentricity and vertex at

Find an equation of the conic satisfying the given conditions.Hyperbola, foci (5, 6) ptotes x = 2y + 3 and

Eliminate the parameter to find a Cartesian equation of the curve.

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

Select the correct Answer: for each question. -Find the vertices, foci and asymptotes of the hyperbola.

The planet Mercury travels in an elliptical orbit with eccentricity Its minimum distance from the Sun is km.If the perihelion distance from a planet to the Sun is and the aphelion distance is , find the maximum distance (in km) from Mercury to the Sun.

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 hyperbola centered at the origin that satisfies the given condition. ptotes:

Find the surface area generated by rotating the lemniscate about the line

Find an equation of the hyperbola with vertices and asymptotes

Find the area of the region that lies inside both curves.