Assignment.1-.3 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the arch. The width 1) of the roadway is 30 feet and the height of the arch over the center of the roadway is feet. Two trucks plan to use this road. They are both 10 feet wide. Truck 1 has an overall height of feet and Truck 2 has an overall height of 8 feet. Draw a rough sketch of the situation and determine which of the trucks can pass under the bridge. A) Truck 1 can pass under the bridge, but Truck 2 cannot. B) Both Truck 1 and Truck 2 can pass under the bridge. C) Neither Truck 1 nor Truck 2 can pass under the bridge. D) Truck 2 can pass under the bridge, but Truck 1 cannot. 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. 2) x2 + y2 = 25 25x2 + 16y2 = 400 2) A) {(0, 5), (0, -5)} B) {(4, 0), (-4, 0)} C) {(0, 4), (0, -4)} D) {(5, 0), (-5, 0)} Find the standard form of the equation of the ellipse satisfying the given conditions. 3) Foci: (-2, 0), (2, 0); x-intercepts: -3 and 3 3) A) x 2 5 + y 2 = 1 B) x 2 4 + y 2 5 = 1 C) x 2 + y 2 5 = 1 D) x 2 4 + y 2 = 1 4) Endpoints of major axis: (-2, 1) and (-2, 7); endpoints of minor axis: (-4, 4) and (0, 4); 4) A) (x - 2) 2 4 C) (x - 2) 2 4 + (y + 4) 2 + (y - 3) 2 = 1 B) (x - 4) 2 4 = 1 D) (x + 2) 2 4 + (y + 2) 2 + (y - 4) 2 = 1 = 1 1
Find the foci of the ellipse whose equation is given. 5) 25(x + 1)2 + 36(y - 1)2 = 00 5) A) foci at (1 + 11, -1) and (1-11, -1) B) foci at (- 11, 1) and ( 11, 1) C) foci at (-1 + 11, -1) and (-1-11, -1) D) foci at (-1 + 11, 1) and (-1-11, 1) 6) 36(x - 2)2 + (y + 3)2 = 324 6) A) foci at (2, -3-3 3) and (2, -3 + 3 3) B) foci at (3, -3-3 3) and (3, -3 + 3 3) C) foci at (-2, -3-3 3) and (-2, -3 + 3 3) D) foci at (-3, 2-3 3) and (-3, 2 + 3 3) Solve the problem. 7) The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the arch. The width 7) of the roadway is 40 feet and the height of the arch over the center of the roadway is 12 feet. Two trucks plan to use this road. They are both 8 feet wide. Truck 1 has an overall height of 11 feet and Truck 2 has an overall height of 12 feet. Draw a rough sketch of the situation and determine which of the trucks can pass under the bridge. A) Truck 1 can pass under the bridge, but Truck 2 cannot. B) Both Truck 1 and Truck 2 can pass under the bridge. C) Truck 2 can pass under the bridge, but Truck 1 cannot. D) Neither Truck 1 nor Truck 2 can pass under the bridge. Find the standard form of the equation of the ellipse and give the location of its foci. 8) 8) A) x 2 4 + y 2 64 = 1 foci at (0, 8) and (2, 0) C) x 2 4 + y 2 64 = 1 foci at (0, -8) and (0, 8) B) x2 64 + y 2 4 = 1 foci at (0, -2 15) and (0, 2 15) D) x 2 4 + y 2 64 = 1 foci at (0, -2 15) and (0, 2 15) 2
Convert the equation to the standard form for an ellipse by completing the square on x and y. ) 36x2 + 16y2 + 72x + 6y - 36 = 0 ) A) (x + 1) 2 36 C) (x + 1) 2 16 + (y + 3) 2 16 + (y + 3) 2 36 = 1 B) (x + 3) 2 16 = 1 D) (x - 1) 2 16 + (y + 1) 2 36 + (y - 3) 2 36 = 1 = 1 Graph the ellipse and locate the foci. 10) x2 = 144-16y2 10) A) foci at (4, 0) and (-4, 0) B) foci at (5, 0) and (-5, 0) C) foci at ( 7, 0) and (- 7, 0) D) foci at (0, 7) and (0, - 7) 3
Solve the problem. 11) Two LORAN stations are positioned 280 miles apart along a straight shore. A ship records a time 11) difference of 0.0007 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) 50 miles from the master station, (100, 123.1) B) 50 miles from the master station, (123.1, 100) C) 0 miles from the master station, (123.1, 100) D) 0 miles from the master station, (100, 123.1) Find the vertices and locate the foci for the hyperbola whose equation is given. 12) 4y2-100x2 = 400 12) A) vertices: (-10, 0), (10, 0) foci: (- 14, 0), ( 14, 0) C) vertices: (0, -10), (0, 10) foci: (0, - 14), (0, 14) B) vertices: (-7, 0), (7, 0) foci: (- 51, 0), ( 51, 0) D) vertices: (0, -7), (0, 7) foci: (0, - 14), (0, 14) Find the standard form of the equation of the hyperbola. 13) 13) A) x 2 4 - y 2 16 = 1 B) y 2 16 - x 2 4 = 1 C) x 2 16 - y 2 4 = 1 D) y 2 4 - x 2 16 = 1 Use the center, vertices, and asymptotes to graph the hyperbola. 4
14) (y + 2) 2 - (x + 1) 2 = 1 14) 4 25 A) B) C) D) 5
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. 15) x2 - y2 = 1 15) x2 + y2 = 1 A) {(0, 1), (0, -1)} B) {(0, 1)} C) {(1, 0), (-1, 0)} D) {(1, 0)} Use vertices and asymptotes to graph the hyperbola. Find the equations of the asymptotes. 16) x 2 - y 2 36 = 1 16) A) Asymptotes: y = ± 2x B) Asymptotes: y = ± 1 2 x 6
C) Asymptotes: y = ± 1 x D) Asymptotes: y = ± 2x 2 Solve the problem. 17) A satellite following the hyperbolic path shown in the picture turns rapidly at (0, 2) and then 17) moves closer and closer to the line y = 3 x as it gets farther from the tracking station at the origin. 2 Find the equation that describes the path of the satellite if the center of the hyperbola is at (0, 0). (0, 2) y = 3 2 x A) y 2 16 - x 2 4 = 1 B) x 2 4 - y2 ( 18 = 1 C) )2 4 y2 4 - x 2 16 = 1 D) x2 ( 18-4 )2 y2 4 = 1 Find the location of the center, vertices, and foci for the hyperbola described by the equation. 18) (y - 3)2-100(x + 1)2 = 100 18) A) Center: (-1, 3); Vertices: (0, -6) and (0, 14); Foci: (0, 4-101) and (0, 4 + 101) B) Center: (-1, 3); Vertices: (-1, -7) and (-1, 13); Foci: (-1, 3-101) and (-1, 3 + 101) C) Center: (-1, 3); Vertices: (1, -10) and (-1, 10); Foci: (-1, - 101) and (-1, 101) D) Center: (1, -3); Vertices: (1, -13) and (1, 7); Foci: (1, -3-101) and (1, -3 + 101) 7
Solve the problem. 1) Two recording devices are set 2400 feet apart, with the device at point A to the west of the device at 1) 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) 1000 feet B) 252.82 feet C) 1612.45 feet D) 1131.37 feet Find the standard form of the equation of the hyperbola satisfying the given conditions. 20) Foci: (0, -4), (0, 4); vertices: (0, -3), (0, 3) 20) A) x 2 - y 2 16 = 1 B) x 2 - y 2 7 = 1 C) y 2 - x 2 16 = 1 D) y 2 - x 2 7 = 1 Determine the direction in which the parabola opens, and the vertex. 21) y = x2 + 6x + 14 21) A) Opens upward; (3, 5) B) Opens upward; (-3, 5) C) Opens to the right; (5, -3) D) Opens to the right; (5, 3) 8
Graph the parabola with the given equation. 22) (x + 1)2 = -7(y - 1) 22) A) B) C) D)
Graph the parabola. 23) y2 = 16x 23) A) B) C) D) Find the vertex, focus, and directrix of the parabola with the given equation. 24) (x + 1)2 = -20(y - 3) 24) A) vertex: (1, -3) focus: (1, -8) directrix: y = 2 C) vertex: (-1, 3) focus: (-1, -2) directrix: y = 8 B) vertex: (-1, 3) focus: (-1, 8) directrix: x = -2 D) vertex: (3, -1) focus: (3, -6) directrix: y = 4 10
Use the vertex and the direction in which the parabola opens to determine the relation's domain and range. 25) x = -(y + 2)2-8 25) A) Domain: (-, -8] Range: (-, ) C) Domain: (-, -8) Range: (-, ) B) Domain: (-, ) Range: (-, ) D) Domain: (-, ) Range: (-, -8] Solve the problem. 26) A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 14 feet and a 26) maximum height of 35 feet. Find the height of the arch at 15 feet from its center. A) 17.8 ft B) 0.2 ft C) 34.2 ft D) 3.3 ft Find the standard form of the equation of the parabola using the information given. 27) Focus: (-1, 0); Directrix: x = 1 27) A) y2 = 4x B) x2 = -4y C) y2 = -1x D) y2 = -4x 28) Vertex: (6, -4); Focus: (3, -4) 28) A) (y + 4)2 = -12(x - 6) B) (x + 6)2 = -4(y - 4) C) (x + 6)2 = 4(y - 4) D) (y + 4)2 = 12(x - 6) 11
Graph the parabola. 2) x2 = 18y 2) A) B) C) D) Find the focus and directrix of the parabola with the given equation. 30) x2 = 32y 30) A) focus: (0, 8) directrix: y = -8 B) focus: (0, -8) directrix: x = -8 C) focus: (8, 0) directrix: y = 8 D) focus: (8, 0) directrix: x = 8 12