Exam 10: Parametric Equations and Polar Coordinates

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.

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

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

The curve cross itself at some point Find the equations of both tangent lines at that point.

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

Select the correct Answer: for each question. -Find an equation of the hyperbola centered at the origin that satisfies the given condition. ptotes:

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.

Set up, but do not evaluate, an integral that represents the length of the parametric curve.

Suppose a planet is discovered that revolves around its sun in an elliptical orbit with the sun at one focus.Its perihelion distance (minimum distance from the planet to the sun) is approximately km, and its aphelion distance (maximum distance from the planet to the sun) is approximately km.Approximate the eccentricity of the planet's orbit.Round to three decimal places.

Find the point(s) on the curve where the tangent is horizontal.

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

Select the correct Answer: for each question -Write a polar equation in nd f an ellipse with the focus at the origin, with the eccentricity and directrix

Find the point(s) of intersection of the curves and

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.

Find the point(s) on the curve where the tangent is horizontal.Select the correct Answer

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

Select the correct Answer: for each question. -Find the point(s) of intersection of the curves and

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

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