Exam 10: Parametric Equations and Polar Coordinates

Graph of the following curve is given.Find its length.Select the correct Answer

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

Find an equation of the conic satisfying the given conditions.Hyperbola, foci (5, 6) ptotes x = 2y + 1 and

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

Find an equation for the conic that satisfies the given conditions.hyperbola, foci , vertices (0, ±

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.Select the correct Answer

Select the correct Answer: for each question. -Find the eccentricity of the conic.

Find an equation for the conic that satisfies the given conditions.Select the correct Answerparabola, vertex (0, 0), focus

Select the correct Answer: for each question -Find an equation of the parabola with focus and directrix

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 vertices, foci, and asymptotes of the hyperbola.

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

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

Find a Cartesian equation for the curve described by the given polar equation.

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

The point in a lunar orbit nearest the surface of the moon is called perilune and the point farthest from the surface is called apolune.The Apollo 11 spacecraft was placed in an elliptical lunar orbit with perilune altitude and apolune altitude (above the moon).Find an equation of this ellipse if the radius of the moon is and the center of the moon is at one focus.

Select the correct Answer: for each question -The curve cross itself at some point Find the equations of both tangent lines at that point.

Find an equation of the hyperbola with vertices and asymptotes

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

Find the polar equation for the curve represented by the given Cartesian equation.Select the correct Answer