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Bartleby Sitemap - Textbook Solutions

All Textbook Solutions for College Algebra (MindTap Course List)

97E In Exercises 95-98, match the equation of the parabola with its graph. y2=9x a. b. c. d.99E 100E 101E 102E Self Check Find an equation in the standard form of the ellipse with center at the origin, major axis of length 10 on the y axis, and minor axis of length 8.2SC 3SC 4SC 5SC 6SC 7SC 1E 2E 3E 4E 5E 6E 7E 8E 9E 10E 11E 12E 13E 14E 15E 16E 17E 18E 19E 20E 21E 22E 23E 24E 25E 26E 27E 28E 29E 30E 31E 32E Graph each ellipse. x225+y29=1 Graph each ellipse. x236+y225=1 Graph each ellipse. x225+y249=1 Graph each ellipse. 4x2+y2=4 Graph each ellipse. x216+(y+2)236=1 Graph each ellipse. (x1)2+4y225=4 Graph each ellipse. (x4)249+(y2)29=1 Graph each ellipse. (x1)225+y24=1 Write each ellipse in standard form. 4x2+y22y=15 42E Write each ellipse in standard form. 9x2+4y2+18x+16y11=0 44E Graph each ellipse. x2+4y24x+8y+4=0 46E 47E 48E 49E 50E Pool tables Find an equation in standard form of the outer edge of the elliptical pool table shown below.52E 53E 54E 55E 56E 57E 58E 59E 60E 61E 62E Discovery and Writing If F is a focus of the ellipse shown and P is any point on the ellipse, use the distance formula to show that the length of FB is acax . Hint: In an ellipse, c2=a2b2 .Finding the focal width In the ellipse shown, chord AA passes through the focus F and is perpendicular to the major axis. Show that the length of AA called the focal width is 2b2a.Prove that segment FV in Example 7 is the shortest distance between the Earth and the Sun. Hint: Refer to Exercise 63. EXAMPLE 7 The orbit of the Earth is approximately an ellipse, with the sun at one focus. The ratio of c to a called the eccentricity of the ellipse is about 162, and the length of the major axis is approximately 186,000,000 miles. How close does the Earth get to the sun?66E The distance between point P(x,y) and the point (0,2) is 13 of the distance of point P from the line y=18. Find an equation in standard form of the ellipse on which point P lies.68E 69E 70E 71E 72E 73E 74E 75E 76E 77E 78E Write an equation in standard form of the hyperbola with vertices (0,4) and (0,4) and a focus at (0,5).2SC 3SC 4SC 1E 2E 3E 4E 5E 6E 7E 8E 9E 10E 11E 12E 13E 14E 15E 16E 17E 18E 19E 20E 21E 22E 23E 24E 25E 26E 27E 28E 29E 30E 31E 32E Write an equation in standard form of each hyperbola described. Vertex (6,0);one end of conjugate axis at (0,54)34E Graph each hyperbola. x29y24=1 36E Graph each hyperbola. 4x23y2=36 Graph each hyperbola. 3x24y2=36 Graph each hyperbola. y2x2=1 Graph each hyperbola. x2y24=1 Graph each hyperbola. (x+2)92y24=1 Graph each hyperbola. y29(x2)236=1 Graph each hyperbola. 4(y2)29(x+1)2=36 44E 45E 46E 47E 48E 49E 50E 51E 52E 53E 54E 55E 56E 57E Astronomy Some comets have a hyperbolic orbit, with the sun as one focus. When the comet shown in the illustration is far away from Earth, it appears to be approaching Earth along the line y=2x . Find the equation in standard form of its orbit if the comet comes within 100 million miles of Earth.59E 60E Navigation The LORAN LOng RAnge Navigation system in the illustration uses two radio transmitters 26 miles apart to send simultaneous signals. The navigator on a ship at P(x,y) receives the closer signal rst and determines that the difference of the distances between the ship and each transmitter is 24 miles. That places the ship on a certain curve. Identify the curve and nd an equation in standard form.62E 63E Sonic boom The position of a sonic boom caused by the faster-than-sound aircraft is one branch of the hyperbola y2x2=25 in the coordinate system shown. How wide is the hyperbola 5 miles from its vertex?Discovery and Writing Describe a hyperbola.66E 67E 68E 69E 70E 71E 72E 73E 74E 75E 76E 77E 78E 79E 80E 1SC 2SC 3SC 4SC 5SC 1E 2E 3E 4E 5E 6E 7E 8E 9E 10E 11E 12E 13E 14E 15E 16E 17E 18E 19E 20E 21E 22E 23E 24E 25E 26E 27E 28E 29E 30E 31E 32E 33E 34E 35E 36E 37E 38E 39E 40E 41E 42E 43E 44E 45E 46E 47E 48E 49E 50E 51E 52E 53E 54E 55E 56E 57E 58E 59E 60E 61E 62E 63E Determine if the statement is true or false. If the statement is false, then correct it and make it true. It is possible for a system of two equations and two variables whose graphs are a hyperbola and an ellipse to have exactly five real ordered pair solutions.65E 66E 1E 2E 3E 4E 5E 6E 7E 8E 9E 10E 11E 12E 13E 14E 15E 16E 17E 18E 19E 20E 21E 22E 23E 24E 25E 26E 27E 28E 29E 30E 1CT 2CT 3CT 4CT 5CT 6CT 7CT 8CT 9CT 10CT 11CT 12CT 13CT 14CT 15CT 16CT Solve each system using substitution and elimination. {x2+y2=23y=x23 18CT 19CT 20CT 1CM 2CM 3CM 4CM

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