Exam 10: Parametric Equations and Polar Coordinates

Select the correct Answer: for each question -In the LORAN (LOng RAnge Navigation) radio navigation system, two radio stations located at and transmit simultaneous signals to a ship or an aircraft located at The onboard computer converts the time difference in receiving these signals into a distance difference and this, according to the definition of a hyperbola, locates the ship or aircraft on one branch of a hyperbola (see the figure).Suppose that station is located mi due east of station on a coastline.A ship received the signal from microseconds efore it received the signal from .Assuming that radio signals travel at a speed of and if the ship is due north of , how far off the coastline is the ship? Round yourAnswer to the nearest mile.

Find the exact area of the surface obtained by rotating the given curve about the x-axis.

True or False? If the parametric curve satisfies then it has a horizontal tangent when

Find the exact area of the surface obtained by rotating the given curve about the x-axis.

Match the equation with the correct graph.

Write a polar equation in and f an ellipse with the focus at the origin, with the eccentricity and directrix

Find an equation of the ellipse that satisfies the given conditions.Foci: (0, ± 1), vertices

Find an equation of the tangent to the curve at the point by first eliminating the parameter.

Select the correct Answer: for each question -Write a polar equation in r and of an ellipse with the focus at the origin, with the eccentricity and vertex at

Find the eccentricity of the conic.Select the correct Answer

The graph of the following curve is given.Find the area that it encloses.

Find the point(s) of intersection of the curves

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

Select the correct Answer: for each question -Find an equation for the conic that satisfies the given conditions.ellipse, foci length of major axis 8

Select the correct Answer: for each question -If a projectile is fired with an initial velocity of meters per second at an angle above the horizontal and air resistance is assumed to be negligible, then its position after t seconds is given by the parametric equations where g is the acceleration of gravity If a gun is fired with and when will the bullet hit the ground?

Select the correct Answer: for each question -Describe the motion of a particle with position as varies in the given interval

Find an equation of the hyperbola centered at the origin that satisfies the given condition. ptotes:

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.

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

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