Question : Use vertices and asymptotes to graph the hyperbola. Find the equations of the asymptotes. 22) 4x^2 - 9y^2 = 36 : 2151876
Use vertices and asymptotes to graph the hyperbola. Find the equations of the asymptotes.
22) 4x2 - 9y2 = 36
A) Asymptotes: y = ± (3/2)x
B) Asymptotes: y = ± (3/2)x
C) Asymptotes: y = ± (2/3)x
D) Asymptotes: y = ± (2/3)x
23) 4y2 - 9x2 = 36
A) Asymptotes: y = ± (3/2)x
B) Asymptotes: y = ± (3/2)x
C) Asymptotes: y = ± (2/3)x
D) Asymptotes: y = ± (2/3)x
24) y = ± √(x2 - 5)
A) Asymptotes: y = ± (3/5)x
B) Asymptotes: y = ± x
C) Asymptotes: y = ± x
D) Asymptotes: y = ± (5/3)x
Find the location of the center, vertices, and foci for the hyperbola described by the equation.
25) ((x - 2)2/25) - ((y + 3)2/4) = 1
A) Center: (2, -3); Vertices: (-2, -3) and (8, -3); Foci: (3 + √(29), -2) and (-2 + √(29), -2)
B) Center: (2, -3); Vertices: (-3, 3) and (7, 3); Foci: (2 - √(29), 3) and (2 + √(29), 3)
C) Center: (-2, 3); Vertices: (-7, 3) and (3, 3); Foci: (-2- √(29), 3) and (-2 + √(29), 3)
D) Center: (2, -3); Vertices: (-3, -3) and (7, -3); Foci: (2 - √(29), -3) and (2 + √(29), -3)
26) ((y + 4)2/9) - ((x - 2)2/25) = 1
A) Center: (2, -4); Vertices: (7, -6) and (3, 0); Foci: (7, -3 - √(34)) and (3, -3 + √(34))
B) Center: (-2, 4); Vertices: (-2, 1) and (-2, 7); Foci: (-2, 4 - √(34)) and (-2, 4 + √(34))
C) Center: (2, -4); Vertices: (2, -4 - √(34)) and (2, -4 + √(34)); Foci: (2, -7) and (2, -1)
D) Center: (2, -4); Vertices: (2, -7) and (2, -1); Foci: (2, -4 - √(34)) and (2, -4 + √(34))
27) (x + 3)2 - 64(y - 4)2 = 64
A) Center: (-3, 4); Vertices: (-10, 5) and (6, 5); Foci: (-2 - √(65), 5) and (-2 + √(65), 5)
B) Center: (-3, 4); Vertices: (8, 4) and (-8, 4); Foci: (- √(65), 4) and (√(65), 4)
C) Center: (3, -4); Vertices: (-5, -4) and (11, -4); Foci: (3 - √(65), 4) and (3 + √(65), 4)
D) Center: (-3, 4); Vertices: (-11, 4) and (5, 4); Foci: (-3 - √(65), 4) and (-3 + √(65), 4)
28) (y - 4)2 - 81(x + 4)2 = 81
A) Center: (4, -4); Vertices: (4, -13) and (4, 5); Foci: (4, -4 - √(82)) and (4, -4 + √(82))
B) Center: (-4, 4); Vertices: (4, -9) and (-4, 9); Foci: (-4, - √(82)) and (-4, √(82))
C) Center: (-4, 4); Vertices: (-4, -5) and (-4, 13); Foci: (-4, 4 - √(82)) and (-4, 4 + √(82))
D) Center: (-4, 4); Vertices: (-3, -4) and (-3, 14); Foci: (-3, 5 - √(82)) and (-3, 5 + √(82))
Use the center, vertices, and asymptotes to graph the hyperbola.
29) ((x - 1)2/9) - ((y - 2)2/16) = 1
A)
B)
C)
D)
30) ((y + 1)2/4) - ((x + 1)2/16) = 1
A)
B)
C)
D)
31) (x + 2)2 - 4(y + 2)2 = 4
A)
B)
C)
D)
32) (y - 4)2 - 9(x + 2)2 = 9
A)
B)
C)
D)
33) (y - 2)2 - (x + 1)2 = 4
A)
B)
C)
D)
Solve the problem.
34) Two LORAN stations are positioned 296 miles apart along a straight shore. A ship records a time difference of 0.00118 seconds between the LORAN signals. (The radio signals travel at 186,000 miles per second.) Where will the ship reach shore if it were to follow the hyperbola corresponding to this time difference? If the ship is 100 miles offshore, what is the position of the ship?
A) 110 miles from the master station, (100, 156.3)
B) 110 miles from the master station, (156.3, 100)
C) 38 miles from the master station, (156.3, 100)
D) 38 miles from the master station, (100, 156.3)
35) Two recording devices are set 3200 feet apart, with the device at point A to the west of the device at point B. At a point on a line between the devices, 400 feet from point B, a small amount of explosive is detonated. The recording devices record the time the sound reaches each one. How far directly north of site B should a second explosion be done so that the measured time difference recorded by the devices is the same as that for the first detonation?
A) 933.33 feet
B) 1549.19 feet
C) 4098.78 feet
D) 1763.83 feet
36) A satellite following the hyperbolic path shown in the picture turns rapidly at (0, 2) and then moves closer and closer to the line y = (8/5)x as it gets farther from the tracking station at the origin. Find the equation that describes the path of the satellite if the center of the hyperbola is at (0, 0).
A) (y2/4) - (x2/(25/16)) = 1
B) (x2/4) - (y2/((32/5))2) = 1
C) (x2/((32/5))2) - (y2/4) = 1
D) (y2/(25/16)) - (x2/4) = 1
Use the relation's graph to determine its domain and range.
37) (x2/9) - (y2/25) = 1
A) Domain: (-∞, ∞)
Range: (-∞, -3) or (3, ∞)
B) Domain: (-∞, -3] and [3, ∞)
Range: (-∞, ∞)
C) Domain: (-∞, -3] or [3, ∞)
Range: (-∞, ∞)
D) Domain: (-∞, ∞)
Range: (-∞, ∞)
38) (x2/9) + (y2/4) = 1
A) Domain: (-3, 3)
Range: (-2, 2)
B) Domain: [-3, 3]
Range: (-∞, ∞)
C) Domain: [-2, 2]
Range: [-3, 3]
D) Domain: [-3, 3]
Range: [-2, 2]
39) (y2/9) - (x2/16) = 1
A) Domain: (-∞, ∞)
Range: (-∞, -3] or [3, ∞)
B) Domain: (-∞, -3] or [3, ∞)
Range: (-∞, ∞)
C) Domain: (-∞, ∞)
Range: (-∞, -3] and [3, ∞)
D) Domain: (-∞, -3] and [3, ∞)
Range: (-∞, ∞)
Find the solution set for the system by graphing both of the system's equations in the same rectangular coordinate system and finding points of intersection.
40) x2 - y2 = 49
x2 + y2 = 49
A) {(7, 0)}
B) {(0, 7)}
C) {(0, 7), (0, -7)}
D) {(7, 0), (-7, 0)}
41) 9x2 + y2 = 9
y2 - 9x2 = 9
A) {(0, -3), (0, 3)}
B) {(0, 9)}
C) {(3, 0), (3, 0)}
D) {(0, -3)}
