Conic Section Applications Number 2

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Slide 1  Conic Section Applications

Slide 2  1. Raul and his friends are having a pizza party and will decide where to have the party based on the delivery area of the pizza restaurant. Suppose that the pizza restaurant is located at the point (1, 2) and the letters represent the homes of Raul and his friends. Use the equation of a circle to find the houses that are within a 3mile radius and will get free delivery.

Slide 3  2. In “whispering galleries” a sound made at one focus can be clearly heard at the other focus, even though very little can be heard by someone in between. Suppose an elliptical room measures 320 ft long and 150 ft wide. How far would the listener have to be from the source of the sound in order to hear it?
 320 ft
 150 ft
 2a
 2b
 2c

Slide 4  3. In some solar collectors, a mirror with a parabolic cross section is used to concentrate sunlight on a pipe, which is located at the focus of a mirror. Suppose the pipe is located 6 ft from the vertex of the mirror. Write an equation of the parabola that models the cross section of the mirror.

Slide 5  Hyperbolas Continued…
 d1
 d2

Slide 6  4. You and a friend live 4 miles apart ( on the same east / west street) and are talking on the phone. You hear a clap of thunder from a lightening storm, and 18 seconds later, your friend hears the thunder. Find an equation that gives the possible places where the lightening could have occurred ( assume the coordinate system is measured in feet and that sound travels 1100 feet per second ). Also remember that 1 mile= 5280 feet
 4 mi
 d1
 d2
 (You)
 (Friend)
 (0,0)

Slide 7  5. A tour boat travels around a small island in a pattern that can be modeled by the equation , with the island at the origin. Suppose that a fishing boat approaches the island on a path that can be modeled by the equation . Is there any danger of collision?
 Yes, there could be a collision since the paths cross. The boats would have to be there at the same time.

Slide 8
 6.

Slide 9
 7.

Slide 10  Try This!!
 Find the equation of a parabola through the points: (2,9), (2,3), and (1,3) using matrices.
 Your teacher was typing a problem on this test. She accidentally deleted most of the problem. The only thing she had left was that the eccentricity= .74. What her original problem an ellipse or a hyperbola?