Precalculus: Graphical, Numerical, Algebraic 8th Edition solutions

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1 and 2, find the distance between the given points. 1-3 -2 21

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1 and 2, find the distance between the given points. 1-3 -4 21

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3 and 4, solve for y in terms of x.2 9 + x 2 4 = 1

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3 and 4, solve for y in terms of x.x 2 36 + y2 25 = 1 y

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 58, solve for x algebraically.13x + 12 + 13x - 8 = 10

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 58, solve for x algebraically.16x + 12 - 14x + 9 = 1

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 58, solve for x algebraically.26x 2 + 12 + 26x 2 + 1 = 11

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 58, solve for x algebraically.22x 2 + 8 + 23x 2 + 4 = 8

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 9 and 10, find exact solutions by completing the square.2x2 - 6x - 3 = 0

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 9 and 10, find exact solutions by completing the square.2 2x + 4x - 5 = 0

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, find the vertices and foci of the ellipse.x 2 16 + y2 7 = 1

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, find the vertices and foci of the ellipse.y2 25 + x 2 21 = 1

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, find the vertices and foci of the ellipse.y2 36 + x 2 27 = 1

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, find the vertices and foci of the ellipse.x 2 11 + y2 7 = 1

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, find the vertices and foci of the ellipse.3x 2 + 4y2 = 12

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, find the vertices and foci of the ellipse.9x 2 + 4y2 = 36

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 710, match the graph with its equation, given that the tick marks on all axes are 1 unit apart.x 2 25 + y2 16 = 1

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 710, match the graph with its equation, given that the tick marks on all axes are 1 unit apart.y2 36 + x 2 9 = 1

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 710, match the graph with its equation, given that the tick marks on all axes are 1 unit apart.1y - 222 16 + 1x + 322 4 = 1

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 710, match the graph with its equation, given that the tick marks on all axes are 1 unit apart.1x - 122 11 + 1y + 222 = 1

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1116, sketch the graph of the ellipse by hand.x 2 64 + y2 36 = 1

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1116, sketch the graph of the ellipse by hand.x 2 81 + y2 25 = 1

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1116, sketch the graph of the ellipse by hand.y2 9 + x 2 4 = 1

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1116, sketch the graph of the ellipse by hand.y2 49 + x 2 25 = 1

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1116, sketch the graph of the ellipse by hand.1x + 322 16 + 1y - 122 4 = 1

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1116, sketch the graph of the ellipse by hand.x - 122 2 + 1y + 322 4 = 1

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1720, graph the ellipse using a function grapher.x 2 36 + y2 16 = 1

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1720, graph the ellipse using a function grapher.y2 64 + x 2 16 = 1 x

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1720, graph the ellipse using a function grapher.1x + 222 5 + 21y - 122 = 1

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1720, graph the ellipse using a function grapher.1x - 422 16 + 161y + 422 = 8

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2136, find an equation in standard form for the ellipse that satisfies the given conditions.Major axis length 6 on y-axis, minor axis length 4

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2136, find an equation in standard form for the ellipse that satisfies the given conditions.Major axis length 14 on x-axis, minor axis length 10

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2136, find an equation in standard form for the ellipse that satisfies the given conditions.Foci 2, 0 , major axis length 10

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2136, find an equation in standard form for the ellipse that satisfies the given conditions.Foci 0, 3 , major axis length 10

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2136, find an equation in standard form for the ellipse that satisfies the given conditions.Endpoints of axes are 4, 0 and 0, 5

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2136, find an equation in standard form for the ellipse that satisfies the given conditions.Endpoints of axes are 7, 0 and 0, 4

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2136, find an equation in standard form for the ellipse that satisfies the given conditions.Major axis endpoints 0, 6 , minor axis length 8

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2136, find an equation in standard form for the ellipse that satisfies the given conditions.Major axis endpoints 5, 0 , minor axis length 4

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2136, find an equation in standard form for the ellipse that satisfies the given conditions.Minor axis endpoints 0, 4 , major axis length 10

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2136, find an equation in standard form for the ellipse that satisfies the given conditions.Minor axis endpoints 12, 0 , major axis length 26

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2136, find an equation in standard form for the ellipse that satisfies the given conditions.Major axis endpoints 1, and 1, 8 , minor axis length 8

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2136, find an equation in standard form for the ellipse that satisfies the given conditions.Major axis endpoints , and , 7 , minor axis length 4

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2136, find an equation in standard form for the ellipse that satisfies the given conditions.Foci and , major axis endpoints and 16, -42

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2136, find an equation in standard form for the ellipse that satisfies the given conditions.Foci and , major axis endpoints and 1-2, 72

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2136, find an equation in standard form for the ellipse that satisfies the given conditions.Major axis endpoints and , minor axis length 6

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2136, find an equation in standard form for the ellipse that satisfies the given conditions.Major axis endpoints , 2 and 3, 2 , minor axis length 6

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3740, find the center, vertices, and foci of the ellipse.1x + 122 25 + 1y - 222 16 = 1

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3740, find the center, vertices, and foci of the ellipse.1x - 322 11 + 1y - 522 7 = 1

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3740, find the center, vertices, and foci of the ellipse.1y + 322 81 + 1x - 722 64 = 1

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3740, find the center, vertices, and foci of the ellipse.1y - 122 25 + 1x + 222 16 = 1

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4144, graph the ellipse using a parametric grapher.y2 25 + x 2 4 = 1

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4144, graph the ellipse using a parametric grapher.x 2 30 + y2 20 = 1

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4144, graph the ellipse using a parametric grapher. \(\frac{(x+3)^{2}}{12}+\frac{(y-6)^{2}}{5}=1\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4144, graph the ellipse using a parametric grapher. \(\frac{(y+1)^{2}}{15}+\frac{(x-2)^{2}}{6}=1\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 45 48, prove that the graph of the equation is an ellipse, and find its vertices, foci, and eccentricity. \(9 x^{2}+4 y^{2}-18 x+8 y-23=0\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 45 48, prove that the graph of the equation is an ellipse, and find its vertices, foci, and eccentricity. \(3 x^{2}+5 y^{2}-12 x+30 y+42=0\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 45 48, prove that the graph of the equation is an ellipse, and find its vertices, foci, and eccentricity. \(9 x^{2}+16 y^{2}+54 x-32 y-47=0\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 45 48, prove that the graph of the equation is an ellipse, and find its vertices, foci, and eccentricity. \(4 x^{2}+y^{2}-32 x+16 y+124=0\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 49 and 50, write an equation for the ellipse.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 49 and 50, write an equation for the ellipse.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn Prove that an equation for the ellipse with center (0, 0), foci \((0,\ \pm c)\) and semimajor axis \(a>c \geq 0\) is \(y^{2} / a^{2}+x^{2} / b^{2}=1\), where \(b^{2}=a^{2}-c^{2}\). [Hint: Refer to derivation at the beginning of the section.]

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn Dancing Among the Stars Using the data in Table 8.1, prove that the object with the most eccentric orbit sometimes is closer to the Sun than the planet with the least eccentric orbit.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
The Moons Orbit The Moons apogee (farthest distance from Earth) is 252,710 miles, and perigee (closest distance to Earth) is 221,463 miles. Assuming the Moons orbit of Earth is elliptical with Earth at one focus, calculate and interpret a, b, c, and e.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Hot Mercury Given that the diameter of the Sun is about 1.392 Gm, how close does Mercury get to the Suns surface?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Saturn Find the perihelion and aphelion distances of Saturn.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Venus and Mars Write equations for the orbits of Venus and Mars in the form \(x^{2} / a^{2}+y^{2} / b^{2}=1\).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Sungrazers One comet group, known as the sungrazers, passes within a Suns diameter (1.392 Gm) of the solar surface. What can you conclude about a - c for orbits of the sungrazers?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Halleys Comet The orbit of Halleys comet is 36.18 AU long and 9.12 AU wide. What is its eccentricity?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Lithotripter For an ellipse that generates the ellipsoid of a lithotripter, the major axis has endpoints (-8, 0) and (8, 0). One endpoint of the minor axis is (0, 3.5). Find the coordinates of the foci.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Lithotripter (Refer to Figure 8.21.) A lithotripters shape is formed by rotating the portion of an ellipse below its minor axis about its major axis. If the length of the major axis is 26 in. and the length of the minor axis is 10 in., where should the shock-wave source and the patient be placed for

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Group Activities In Exercises 61 and 62, solve the system of equations algebraically and support your answer graphically. \(\frac{x^{2}}{4}+\frac{y^{2}}{9}=1\) \(x^{2}+y^{2}=4\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Group Activities In Exercises 61 and 62, solve the system of equations algebraically and support your answer graphically. \(\frac{x^{2}}{9}+y^{2}=1\) \(x-3 y=-3\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Group Activity Consider the system of equations \(x^{2}+4 y^{2}=4\) \(y=2 x^{2}-3\) (a) Solve the system graphically. (b) If you have access to a grapher that also does symbolic algebra, use it to find the exact solutions to the system.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn Look up the adjective eccentric in a dictionary and read its various definitions. Notice that the word is derived from ex-centric, meaning out-of-center or off-center. Explain how this is related to the words everyday meanings as well as its mathematical meaning for ellipses.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False The distance from a focus of an ellipse to the closer vertex is a(1 + e), where a is the semimajor axis and e is the eccentricity. Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False The distance from a focus of an ellipse to either endpoint of the minor axis is half the length of the major axis. Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 6770, you may use a graphing calculator to solve the problem. Multiple Choice One focus of \(x^{2}+4 y^{2}=4\) is (A) (4, 0). (B) (2, 0). (C) \((\sqrt{3},\ 0)\) (D) \((\sqrt{2},\ 0)\) (E) (1, 0)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 6770, you may use a graphing calculator to solve the problem. Multiple Choice The focal axis of \(\frac{(x-2)^{2}}{25}+\frac{(y-3)^{2}}{16}=1\) is (A) y = 1. (B) y = 2. (C) y = 3. (D) y = 4. (E) y = 5.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 6770, you may use a graphing calculator to solve the problem. Multiple Choice The center of \(9 x^{2}+4 y^{2}-72 x-24 y+144=0\) is (A) (4, 0). (B) (4, 3). (C) (4, 4). (D) (4, 5). (E) (4, 6).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 6770, you may use a graphing calculator to solve the problem. Multiple Choice The perimeter of a triangle with one vertex on the ellipse \(x^{2} / a^{2}+y^{2} / b^{2}=1\) and the other two vertices at the foci of the ellipse would be (A) a + b. (B) 2a

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Area and Perimeter The area of an ellipse is \(A=\pi a b\), but the perimeter cannot be expressed so simply: \(P \approx \pi(a+b)\left(3-\frac{\sqrt{(3 a+b)(a+3 b)}}{a+b}\right)\) (a) Prove that, when a = b = r, these become the familiar formulas for the area and perimeter (cir

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn Keplers Laws We have encountered Keplers first and third laws (pages 179, 595). Using a library or the Internet, (a) Read about Keplers life, and write in your own words how he came to discover his three laws of planetary motion. (b) What is Keplers Second Law? Explain it wit

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Pendulum Velocity vs. Position As a pendulum swings toward and away from a motion detector, its distance (in meters) from the detector is given by the position function x(t) = 3 + cos (2t - 5), where t represents time (in seconds). The velocity (in m/sec) of the pendulum is given by y(t) = -2 sin (2t

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Pendulum Velocity vs. Position A pendulum that swings toward and away from a motion detector has a distance (in feet) from the detector of \(x(t)=5+3 \sin (\pi t+\pi / 2)\) and a velocity (in ft/sec) of \(y(t)=3 \pi \cos (\pi t+\pi / 2)\) where t represents time (in seconds). (a) Prove that the p

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Prove that a nondegenerate graph of the equation \(A x^{2}+C y^{2}+D x+E y+F=0\) is an ellipse if AC > 0.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn The graph of the equation \(\frac{(x-h)^{2}}{a^{2}}+\frac{(y-k)^{2}}{b^{2}}=0\) is considered to be a degenerate ellipse. Describe the graph. How is it like a full-fledged ellipse, and how is it different?