Summative Test 2: Ellipse, Hyperbola & Application

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What are the asymptotes of the hyperbola?

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P1. A big room is constructed so that the ceiling is a dome that is semi-elliptical in shape. If a person stands at one focus and speaks, the sound that is made bounces off the ceiling and gets reflected in the other focus. Thus, if two people stand at the foci (ignoring their heights), they will be able to hear each other. If the room is 34 m long and 8 m high, how far from the center should each of two people stand if they would like to whisper back and forth and hear each other? (Show your solution in yellow or google docs) ( 2 points)

• A. 15 m

• B. 16 m

• C. 51 m

• D. 61 m

P2. A satellite dish is shaped like a paraboloid. Signals that strike the surface of the dish are reflected in a single point that corresponds to the focus of the parabola. This point is where the receiver should be located. Suppose that the dish is 10 feet across and 3 feet deep at its center, at what position should the receiver be placed? ( Show your complete solution in yellow paper or google docs) (2 points)

• A. 2.08 feet

• B. 0.48 feet

• C. 2.1 feet

• D. 0.45 feet

P3. A single-lane street 12 feet wide goes through a semicircular tunnel with a radius of 9 feet. How high is the tunnel at the edge of each lane? (Show your complete solution in yellow paper or google docs) (2 points)

• A. 9.20 feet

• B. 8.64 feet

• C. 7.48 feet

• D. 6.71 feet

Which of the equations represents an ellipse?

Which of the statements are TRUE about ellipse?

• A. I and II

• B. I and III

• C. II and III

• D. I, II and III

What is the standard equation of the given ellipse?

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Find the standard equation of the given ellipse.

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• A. 1

• B. 5

• C. 16

• D. 25