Mastering Hyperbola Problems: Asymptotes and Applications
Authored by Anthony Clark
English
10th Grade
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A satellite dish is shaped like a hyperbola. If the distance between the foci of the dish is 10 meters and the distance from the center to a vertex is 4 meters, what are the equations of the asymptotes?
y = (5/4)x, y = -(5/4)x
y = (1/2)x, y = -(1/2)x
y = (4/3)x, y = -(4/3)x
y = (3/4)x, y = -(3/4)x
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A hyperbola is used in a cooling tower design. If the transverse axis is 12 meters and the conjugate axis is 16 meters, find the equations of the asymptotes.
y = 4x, y = -4x
y = (3/4)x, y = -(3/4)x
y = (4/3)x, y = -(4/3)x
y = (2/3)x, y = -(2/3)x
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A car is traveling along a road that curves in the shape of a hyperbola. If the distance from the center to a vertex is 5 miles and the distance between the foci is 8 miles, what is the equation of the hyperbola?
(y^2/20) - (x^2/16) = 1
(y^2/30) - (x^2/4) = 1
(y^2/25) - (x^2/9) = 1
(y^2/10) - (x^2/25) = 1
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
An engineer is designing a bridge that resembles a hyperbola. If the distance between the foci is 14 meters and the distance from the center to a vertex is 7 meters, calculate the asymptotes of the hyperbola.
y = 0
y = 7
y = -7
y = 14
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A hyperbola is formed by the path of a satellite. If the distance from the center to a vertex is 3 km and the distance between the foci is 10 km, what are the equations of the asymptotes?
y = 2x + 1 and y = -2x + 1
y = (4/3)x and y = -(4/3)x
y = (3/4)x and y = -(3/4)x
y = (5/3)x and y = -(5/3)x
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A hyperbola is used to model the trajectory of a water fountain. If the transverse axis is 20 feet and the conjugate axis is 30 feet, find the equations of the asymptotes.
y = (1/2)x and y = -(1/2)x
y = (3/2)x and y = -(3/2)x
y = (2/3)x and y = -(2/3)x
y = 3x and y = -3x
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A hyperbola is used in a physics experiment to study sound waves. If the distance between the foci is 12 meters and the distance from the center to a vertex is 6 meters, what is the equation of the hyperbola?
y^2/36 - x^2/0 = 1
y^2/36 - x^2/12 = 1
y^2/36 + x^2/0 = 1
y^2/24 - x^2/0 = 1
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