Exam 10: Parametric Equations and Polar Coordinates

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

Find the equation of the directrix of the conic.

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. -Find parametric equations to represent the line segment from

In the LORAN (LOng RAnge Navigation) radio navigation system, two radio stations located at A and B transmit simultaneous signals to a ship or an aircraft located at P.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 B is located L = mi due east of station A on a coastline.A ship received the signal from B microseconds before it received the signal from A.Assuming that radio signals travel at a speed of and if the ship is due north of B, how far off the coastline is the ship? Round yourAnswer to the nearest mile.Select the correct Answer

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

True or False? The exact length of the parametric curve

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

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

Select the correct Answer: for each question. -Find the length of the polar curve.

Find parametric equations to represent the line segment from Select the correct Answer

True or False? The exact length of the parametric curve

Find the area of the region that is bounded by the given curve and lies in the specified sector.

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

Find the area enclosed by the curve

Select the correct Answer: for each question. -Find the point(s) on the curve where the tangent is horizontal.

Select the correct Answer: for each question -Sketch the polar curve with the given equation.

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

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

Select the correct Answer: for each question -Find the area of the region that lies inside the first curve and outside the second curve.