Applications of Circles and Ellipses

Planets orbit the Sun in a shape called a(n)

• circle
• ellipse
• focus
• perihelion

A rabbit will move no more than 10 miles away from its hole (located at the origin). At a particular time, you are taking a walk about 5 miles east and 7 miles north of the rabbit hole. Is there any possibility of you meeting the rabbit?

• Yes, because you would be 8.6 miles away.

• Yes, because you would be 7.4 miles away.

• No, because you would be 37 miles away.

• No, because you would be 74 miles away.

• Jadin

• Emily

• Madison

• Dominic

A radio tower services an area of 380.133 square miles. You stop your car 4 miles east and 9 miles north of the tower. Will you be able to receive radio waves from the tower?  (The base of the tower is located at the origin.)

• Yes, because 97<121

• Yes, because 81<121

• No, because 121>97

• No, because 380>97

A communications satellite has been placed in an elliptical orbit around Earth.  The satellite’s orbital path is directly above the equator.  One focus is at Earth’s center, and each focus is 410 km from the center of the ellipse.  The length of the major axis is 13,960 km. What is an equation that describes the satellite's orbit?

 

A communications satellite has been placed in an elliptical orbit around Earth.  The satellite’s orbital path is directly above the equator.  One focus is at Earth’s center, and each focus is 410 km from the center of the ellipse.  The length of the major axis is 13,960 km. How does the satellite's orbit compare to a circular orbit?

• The orbit is close to circular because the foci are close together.

• The orbit is much flatter because the foci are far apart.

• The orbit is close to circular because the foci are far apart.

• The orbit is much flatter because the foci are close together.

Olivia, standing at one focus of a whispering gallery, is 6 feet from the nearest wall.  Her friend is standing at the other focus, 100 feet away.  What is the length of the whispering gallery?

• 56 feet long

• 50 feet long

• 112 feet long

• 636 feet long

Olivia, standing at one focus of a whispering gallery, is 6 feet from the nearest wall.  Her friend is standing at the other focus, 100 feet away.  How high is it’s elliptical ceiling at the center?

• 636 feet high

• 50.4 feet high

• 2,544 feet high

• 25.2 feet high

A planet's orbit around the sun is elliptical with the sun at one focus. The maximum distance from the sun (aphelion) of planet Mars is approximately 156 million miles, while its minimum distance from the sun (perihelion) is about 128 million miles.

(A) What is the equation of the elliptical orbit of Mars?

• None of the above choices