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Questions and Answers of College Algebra

Identify the type of graph that each equation has, without actually graphing.y + 7 = 4(x + 3)2
Identify the type of graph that each equation has, without actually graphing. y? x? х 25 25
Identify the type of graph that each equation has, without actually graphing. , (y – 4)² |(x + 2)² 16
Identify the type of graph that each equation has, without actually graphing. y2 x2 16 4
Identify the type of graph that each equation has, without actually graphing.x2 - y2 = 1
Identify the type of graph that each equation has, without actually graphing. y2 %3D 49 100
Identify the type of graph that each equation has, without actually graphing. x? y? 25 36
Identify the type of graph that each equation has, without actually graphing.x - 1 = -3(y - 4)2
Identify the type of graph that each equation has, without actually graphing.x = 3y2 + 5y - 6
Identify the type of graph that each equation has, without actually graphing.y = 2x2 + 3x - 4
Identify the type of graph that each equation has, without actually graphing.(x - 2)2 + (y + 3)2 = 25
Identify the type of graph that each equation has, without actually graphing.x2 + y2 = 144
Identify the type of conic section described.The conic section consisting of the set of points in a plane for which the distance from the point (2, 0) is one-third of the distance from the line x = 10
Identify the type of conic section described.The conic section consisting of the set of points in a plane for which the distance from the point (3, 0) is one and one-half times the distance from the
Identify the type of conic section described.The conic section consisting of the set of points in a plane for which the absolute value of the difference of the distances from the points (3, 0) and
Identify the type of conic section described.The conic section consisting of the set of points in a plane for which the sum of the distances from the points (5, 0) and (5, 0) is 14
Identify the type of conic section described.The conic section with eccentricity e = 0
Identify the type of conic section described.The conic section consisting of the set of points in a plane for which the distance from the point (1, 3) is equal to the distance from the line y = 1
Identify the type of conic section described.The conic section consisting of the set of points in a plane that are equidistant from a fixed point and a fixed line
Identify the type of conic section described.The conic section consisting of the set of points in a plane that lie a given distance from a given point.
The graph of x2/4 - y2 = 1 is a hyperbola. We know that the graph of this hyperbola approaches its asymptotes as 0 x 0 increases without bound. Work Exercises in order, to see the relationship
The graph of x2/4 - y2 = 1 is a hyperbola. We know that the graph of this hyperbola approaches its asymptotes as 0 x 0 increases without bound. Work Exercises in order, to see the relationship
The graph of x2/4 - y2 = 1 is a hyperbola. We know that the graph of this hyperbola approaches its asymptotes as 0 x 0 increases without bound. Work Exercises in order, to see the relationship
The graph of x2/4 - y2 = 1 is a hyperbola. We know that the graph of this hyperbola approaches its asymptotes as 0 x 0 increases without bound. Work Exercises in order, to see the relationship
The graph of x2/4 - y2 = 1 is a hyperbola. We know that the graph of this hyperbola approaches its asymptotes as 0 x 0 increases without bound. Work Exercises in order, to see the relationship
The graph of x2/4 - y2 = 1 is a hyperbola. We know that the graph of this hyperbola approaches its asymptotes as 0 x 0 increases without bound. Work Exercises in order, to see the relationship
Suppose a hyperbola has center at the origin, foci at F′(-c, 0) and F(c, 0), andLet b2 = c2 - a2, and show that an equation of the hyperbola is |d(P, F') – d(P, F)| = 2a. %3D x? y? 1. a? b2
Two buildings in a sports complex are shaped and positioned like a portion of the branches of the hyperbola 400x2 - 625y2 = 250,000, where x and y are in meters.(a) How far apart are the buildings at
A rugby field is similar to a modern football field except that the goalpost, which is 18.5 ft wide, is located on the goal line instead of at the back of the endzone. The rugby equivalent of a
Microphones are placed at points (-c, 0) and (c, 0). An explosion occurs at point P(x, y) having positive x-coordinate. See the figure. The sound is detected at the closer microphone t seconds before
Ships and planes often use a location-finding system called LORAN. With this system, a radio transmitter at M in the figure sends out a series of pulses. When each pulse is received at transmitter S,
In 1911, Ernest Rutherford discovered the basic structure of the atom by "shooting" positively charged alpha particles with a speed of 107 m per sec at a piece of gold foil 6 × 10-7 m thick. Only a
Determine the two equations necessary to graph each hyperbola using a graphing calculator, and graph it in the viewing window indicated. y² – 9x² = 9; [-10, 10] by [– 10, 10]
Determine the two equations necessary to graph each hyperbola using a graphing calculator, and graph it in the viewing window indicated. 4y? — 36х? %3D 144;B [-10, 10] by [— 15, 15]
Determine the two equations necessary to graph each hyperbola using a graphing calculator, and graph it in the viewing window indicated. x2 1; [-10, 10] by 49 [– 10, 10] 25 ||
Determine the two equations necessary to graph each hyperbola using a graphing calculator, and graph it in the viewing window indicated. y2 = 1; [-6.6, 6.6] by [-8, 8] х 4 16 4+
Write an equation for the hyperbola.e = 5/4 ; vertices at (2, 10), (2, 2)
Write an equation for the hyperbola.e = 25/9 ; foci at (9, -1), (-11, -1)
Write an equation for the hyperbola.e = 5/3 ; center at (8, 7); focus at (3, 7)
Write an equation for the hyperbola.e = 3; center at (0, 0); vertex at (0, 7)
Write an equation for the hyperbola.Center at (9, -7); focus at (9, -17); vertex at (9, -13)
Write an equation for the hyperbola.Center at (1, -2); focus at (-2, -2); vertex at (-1, -2)
Write an equation for the hyperbola.Vertices at (5, -2), (1, -2); asymptotes y = ±3/2 (x - 3) - 2
Write an equation for the hyperbola.Vertices at (4, 5), (4, 1); asymptotes y = ±7(x - 4) + 3
Write an equation for the hyperbola. (-3V5,0). (3V5,0); asymptotes y = ±2x foci at
Write an equation for the hyperbola. (0, V13). (0, – V13) foci at l; asymptotes y = ±5x|
Write an equation for the hyperbola.Vertices at (0, 5), (0, -5); passing through the point (-3, 10)
Write an equation for the hyperbola.vertices at (-3, 0), (3, 0); passing through the point (-6, -1)
Write an equation for each hyperbola.Vertices at (-10, 0), (10, 0); asymptotes y = ±5x
Write an equation for each hyperbola.Vertices at (0, 6), (0, -6); asymptotes y = ±1/2 x
Write an equation for each hyperbola.y-intercepts (0, ±12); foci at (0, -15), (0, 15)
Write an equation for the hyperbola.x-intercepts (±3, 0); foci at (-5, 0), (5, 0)
Find the eccentricity e of the hyperbola. Round to the nearest tenth.8y2 - 2x2 = 16
Find the eccentricity e of the hyperbola. Round to the nearest tenth.16y2 - 8x2 = 16
Find the eccentricity e of the hyperbola. Round to the nearest tenth. = 1
Graph the equation. Give the domain and range. Identify any that are functions. Зу — V4x — 16
Graph the equation. Give the domain and range. Identify any that are functions. 5x = -V1 + 4y2 | 5х — -Vi +
Graph the equation. Give the domain and range. Identify any that are functions. 3 25
Graph the equation. Give the domain and range. Identify any that are functions. x2 1+ 16 3
Graph the hyperbola. Give the domain, range, center, vertices, foci, and equations of the asymptotes.4(x + 9)2 - 25(y + 6)2 = 100
Graph the hyperbola. Give the domain, range, center, vertices, foci, and equations of the asymptotes.16(x + 5)2 - (y - 3)2 = 1
Graph the hyperbola. Give the domain, range, center, vertices, foci, and equations of the asymptotes. |(y + 5) (x- 1) 16 ||
Graph the hyperbola. Give the domain, range, center, vertices, foci, and equations of the asymptotes. |(x+ 3)2 (y– 2)2 16 = 1
Graph the hyperbola. Give the domain, range, center, vertices, foci, and equations of the asymptotes. |(x+ 6)? (y+ 4)² (y + 4)? 81 144
Graph the hyperbola. Give the domain, range, center, vertices, foci, and equations of the asymptotes. |(y - 7)? (x- 4)2 = 1 36 64
Graph the hyperbola. Give the domain, range, center, vertices, foci, and equations of the asymptotes.25y2 - 9x2 = 1
Graph the hyperbola. Give the domain, range, center, vertices, foci, and equations of the asymptotes.9x2 - 4y2 = 1
Graph the hyperbola. Give the domain, range, center, vertices, foci, and equations of the asymptotes.x2 - 4y2 = 16
Graph the hyperbola. Give the domain, range, center, vertices, foci, and equations of the asymptotes.4y2 - 25x2 = 100
Graph the hyperbola. Give the domain, range, center, vertices, foci, and equations of the asymptotes.4y2 - 16x2 = 64
Graph the hyperbola. Give the domain, range, center, vertices, foci, and equations of the asymptotes.9x2 - 25y2 = 225
Graph the hyperbola. Give the domain, range, center, vertices, foci, and equations of the asymptotes.x2 - 4y2 = 64
Graph the hyperbola. Give the domain, range, center, vertices, foci, and equations of the asymptotes.x2 - y2 = 9
Graph each hyperbola. Give the domain, range, center, vertices, foci, and equations of the asymptotes. y2 x2 = 1 64 4.
Graph each hyperbola. Give the domain, range, center, vertices, foci, and equations of the asymptotes. y² x2 49 25
Graph each hyperbola. Give the domain, range, center, vertices, foci, and equations of the asymptotes. y? = 1 144 x2 %3D 25
Graph each hyperbola. Give the domain, range, center, vertices, foci, and equations of the asymptotes. x? y2 16
Match each equation with the correct graph. y2 = 1 9. x2 25 A. y B. 3 HHН HHН х C. y D. y -5 —х НОКН х -3 3 -3
Match each equation with the correct graph. y? = 1 x2 25 A. y B. 3 HHН HHН х C. y D. y -5 —х НОКН х -3 3 -3
Match each equation with the correct graph. y2 25 A. y B. 3 HHН HHН х C. y D. y -5 —х НОКН х -3 3 -3
Match each equation with the correct graph. х? y2 25 A. y B. 3 HHН HHН х C. y D. y -5 —х НОКН х -3 3 -3
Match each equation of a hyperbola in Column I with its description in Column II. (x + 2)² = 1 |(y + 1)? 25 п A. center (1, 2); horizontal transverse axis B. center (-2, -1); vertical transverse
Match each equation of a hyperbola in Column I with its description in Column II. (x + 1)? (y + 2)? 64 49 п A. center (1, 2); horizontal transverse axis B. center (-2, -1); vertical transverse axis
Match each equation of a hyperbola in Column I with its description in Column II. (y – 2)² |(x – 1)2 64 49 П A. center (1, 2); horizontal transverse axis B. center (-2, –1); vertical
Identify and then graph each conic section. If it is a parabola, give the vertex, focus, directrix, and axis of symmetry. If it is an ellipse, give the center, vertices, and foci.x = -4y2 - 4y - 3
Identify and then graph each conic section. If it is a parabola, give the vertex, focus, directrix, and axis of symmetry. If it is an ellipse, give the center, vertices, and foci. |(x + 3)², (y +
Identify and then graph each conic section. If it is a parabola, give the vertex, focus, directrix, and axis of symmetry. If it is an ellipse, give the center, vertices, and foci.8(x + 1) = (y + 3)2
Identify and then graph each conic section. If it is a parabola, give the vertex, focus, directrix, and axis of symmetry. If it is an ellipse, give the center, vertices, and foci.4x2 + 9y2 = 36
Identify and then graph each conic section. If it is a parabola, give the vertex, focus, directrix, and axis of symmetry. If it is an ellipse, give the center, vertices, and foci.y + 4 = (x + 3)2
Write an equation for each conic section.Ellipse with center (3, -2); a = 5; c = 3; major axis vertical
Write an equation for each conic section.Parabola with vertex at the origin; through the point (√10, -5); opens down
Write an equation for each conic section.Parabola with vertex (-1, 2) and focus (2, 2)
Match each equation of a conic section in Column I with the appropriate description in Column II. II (a) x + 3 = 4(y – 1)² (b) (x + 3)² + (y – 1)² = 81 (c) 25(x – 2)2 + (y – 1)² = 100 (х
Rework Exercise 53 if the equation of the ellipse is 9x2 + 4y2 = 36.Exercise 53 y? = 1. 9 36
Suppose a lithotripter is based on the ellipse with equationHow far from the center of the ellipse must the kidney stone and the source of the beam be placed? Give the exact answer. y2 1. x? 36
(a) The Roman Colosseum is an ellipse with major axis 620 ft and minor axis 513 ft. Find the distance between the foci of this ellipse to the nearest foot.(b) A formula for the approximate perimeter
Neptune and Pluto both have elliptical orbits with the sun at one focus. Neptune’s orbit has a = 30.1 astronomical units (AU) with an eccentricity of e = 0.009, whereas Pluto’s orbit has a = 39.4
The coordinates in miles for the orbit of the artificial satellite Explorer VII can be modeled by the equationwhere a = 4465 and b = 4462. Earth’s center is located at one focus of the elliptical
Solve the problem.The famous Halley’s comet last passed by Earth in February 1986 and will next return in 2062. It has an elliptical orbit of eccentricity 0.9673 with the sun at one focus. The
Solve the problem.An arch has the shape of half an ellipse. The equation of the ellipse is 100x2 + 324y2 = 32,400, where x and y are in meters.(a) How high is the center of the arch?(b) How wide is

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