LC BEG & INT ALGEBRA
6th Edition
ISBN: 9781266315183
Author: Miller
Publisher: MCG
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Chapter 13.3, Problem 12PE
To determine
To graph: The ellipse
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Check out a sample textbook solutionStudents have asked these similar questions
For Exercises 13–22,
a. Identify the center.
b. Identify the vertices.
c. Identify the foci.
d. Write equations for the asymptotes.
e. Graph the hyperbola. (See Examples 1-2)
13.
16
y?
= 1
25
14.
25
y?
= 1
36
y²
15.
4
= 1
36
y?
16.
9.
= 1
49
17. 25y
- 81x = 2025
18. 49y?
16x = 784
19. - 5x? + 7y² = -35
20. –7x + 1ly = -77
21.
25
16y
1
4x?
22.
81
16y?
1
49
225
For Exercises 43–48, the equation represents a conic section (nondegenerative case).
a. Identify the type of conic section. (See Example 6)
b. Graph the equation on a graphing utility.
43. 4x – 4xy + 5y – 20 = 0
44. 6x + 4V3xy + 2y - 18x + 18V3y – 72 = 0
45. 2x – 6xy + 3y²
- 4x + 12y – 9 = 0
46. 5x – 3xy + 2y – 6 = 0
47. 4x + 8xy + 4y – 2x – 5y – 2 = 0
48. 4x? + 8V3xy + 3y + 2x – 12y – 6 = 0
Exercises 45–48 give equations for parabolas and tell how many units up or down and to the right or left each parabola is to be shifted. Find an equation for the new parabola, and find the new vertex, focus, and directrix.
45. y2 = 4x,
46. x2 = 8y, right 1, down 7
47. x2 = 6y, left 2, down 3
48. y2 = -12x, right 4, up 3 left 3, down 2
Chapter 13 Solutions
LC BEG & INT ALGEBRA
Ch. 13.1 - Find the distance between the points ( − 4 , − 2 )...Ch. 13.1 - Prob. 2SPCh. 13.1 - Prob. 3SPCh. 13.1 - Prob. 4SPCh. 13.1 - Prob. 5SPCh. 13.1 - Prob. 6SPCh. 13.1 - Prob. 7SPCh. 13.1 - Prob. 8SPCh. 13.1 - Prob. 1PECh. 13.1 - Prob. 2PE
Ch. 13.1 - Prob. 3PECh. 13.1 - Prob. 4PECh. 13.1 - Prob. 5PECh. 13.1 - Prob. 6PECh. 13.1 - Prob. 7PECh. 13.1 - Prob. 8PECh. 13.1 - Prob. 9PECh. 13.1 - Prob. 10PECh. 13.1 - Prob. 11PECh. 13.1 - Prob. 12PECh. 13.1 - Prob. 13PECh. 13.1 - Prob. 14PECh. 13.1 - Prob. 15PECh. 13.1 - Prob. 16PECh. 13.1 - Prob. 17PECh. 13.1 - Prob. 18PECh. 13.1 - Prob. 19PECh. 13.1 - Prob. 20PECh. 13.1 - Prob. 21PECh. 13.1 - Prob. 22PECh. 13.1 - Prob. 23PECh. 13.1 - Prob. 24PECh. 13.1 - Prob. 25PECh. 13.1 - Prob. 26PECh. 13.1 - Prob. 27PECh. 13.1 - Prob. 28PECh. 13.1 - Prob. 29PECh. 13.1 - Prob. 30PECh. 13.1 - Prob. 31PECh. 13.1 - Prob. 32PECh. 13.1 - Prob. 33PECh. 13.1 - Prob. 34PECh. 13.1 - Prob. 35PECh. 13.1 - Prob. 36PECh. 13.1 - Prob. 37PECh. 13.1 - Prob. 38PECh. 13.1 - Prob. 39PECh. 13.1 - Prob. 40PECh. 13.1 - Prob. 41PECh. 13.1 - Prob. 42PECh. 13.1 - Prob. 43PECh. 13.1 - Prob. 44PECh. 13.1 - Prob. 45PECh. 13.1 - Prob. 46PECh. 13.1 - Prob. 47PECh. 13.1 - Prob. 48PECh. 13.1 - For Exercises 49–54, write an equation that...Ch. 13.1 - Prob. 50PECh. 13.1 - Prob. 51PECh. 13.1 - Prob. 52PECh. 13.1 - Prob. 53PECh. 13.1 - Prob. 54PECh. 13.1 - Prob. 55PECh. 13.1 - Prob. 56PECh. 13.1 - Prob. 57PECh. 13.1 - Prob. 58PECh. 13.1 - Prob. 59PECh. 13.1 - Prob. 60PECh. 13.1 - Prob. 61PECh. 13.1 - Prob. 62PECh. 13.1 - Prob. 63PECh. 13.1 - Prob. 64PECh. 13.1 - Prob. 65PECh. 13.1 - Prob. 66PECh. 13.1 - Prob. 67PECh. 13.1 - Prob. 68PECh. 13.1 - Prob. 69PECh. 13.1 - For Exercises 65–72, find the midpoint of the line...Ch. 13.1 - For Exercise 65-72, find the midpoint of the line...Ch. 13.1 - For Exercise 65-72, find the midpoint of the line...Ch. 13.1 - Prob. 73PECh. 13.1 - Prob. 74PECh. 13.1 - For Exercises 75–78, the two given points are...Ch. 13.1 - Prob. 76PECh. 13.1 - Prob. 77PECh. 13.1 - Prob. 78PECh. 13.1 - Prob. 79PECh. 13.1 - Prob. 80PECh. 13.1 - Prob. 81PECh. 13.1 - Prob. 82PECh. 13.1 - Prob. 83PECh. 13.1 - Prob. 84PECh. 13.1 - Prob. 85PECh. 13.1 - Prob. 86PECh. 13.1 - Prob. 87PECh. 13.1 - Prob. 88PECh. 13.2 - Prob. 1SPCh. 13.2 - Prob. 2SPCh. 13.2 - Prob. 3SPCh. 13.2 - Prob. 4SPCh. 13.2 - Prob. 5SPCh. 13.2 - Prob. 6SPCh. 13.2 - Prob. 7SPCh. 13.2 - Prob. 8SPCh. 13.2 - Prob. 9SPCh. 13.2 - Prob. 10SPCh. 13.2 - Prob. 11SPCh. 13.2 - 1. a. A circle, a parabola, an ellipse, and a...Ch. 13.2 - Prob. 2PECh. 13.2 - Prob. 3PECh. 13.2 - Prob. 4PECh. 13.2 - Prob. 5PECh. 13.2 - Prob. 6PECh. 13.2 - Prob. 7PECh. 13.2 - Prob. 8PECh. 13.2 - Prob. 9PECh. 13.2 - Prob. 10PECh. 13.2 - Prob. 11PECh. 13.2 - Prob. 12PECh. 13.2 - Prob. 13PECh. 13.2 - Prob. 14PECh. 13.2 - Prob. 15PECh. 13.2 - Prob. 16PECh. 13.2 - Prob. 17PECh. 13.2 - Prob. 18PECh. 13.2 - Prob. 19PECh. 13.2 - For Exercises 25–33, determine the vertex by using...Ch. 13.2 - Prob. 21PECh. 13.2 - Prob. 22PECh. 13.2 - Prob. 23PECh. 13.2 - Prob. 24PECh. 13.2 - Prob. 25PECh. 13.2 - Prob. 26PECh. 13.2 - Prob. 27PECh. 13.2 - Prob. 28PECh. 13.2 - Prob. 29PECh. 13.2 - Prob. 30PECh. 13.2 - Prob. 31PECh. 13.2 - Prob. 32PECh. 13.2 - Prob. 33PECh. 13.2 - Prob. 34PECh. 13.2 - Prob. 35PECh. 13.2 - Prob. 36PECh. 13.2 - Prob. 37PECh. 13.2 - Prob. 38PECh. 13.2 - Prob. 39PECh. 13.2 - Prob. 40PECh. 13.2 - Prob. 41PECh. 13.2 - Prob. 42PECh. 13.2 - Prob. 43PECh. 13.3 - Prob. 1SPCh. 13.3 - Prob. 2SPCh. 13.3 - Prob. 3SPCh. 13.3 - Prob. 4SPCh. 13.3 - Prob. 5SPCh. 13.3 - Prob. 1PECh. 13.3 - Prob. 2PECh. 13.3 - Prob. 3PECh. 13.3 - Prob. 4PECh. 13.3 - Prob. 5PECh. 13.3 - Prob. 6PECh. 13.3 - Prob. 7PECh. 13.3 - Prob. 8PECh. 13.3 - Prob. 9PECh. 13.3 - Prob. 10PECh. 13.3 - Prob. 11PECh. 13.3 - Prob. 12PECh. 13.3 - Prob. 13PECh. 13.3 - Prob. 14PECh. 13.3 - Prob. 15PECh. 13.3 - Prob. 16PECh. 13.3 - Prob. 17PECh. 13.3 - Prob. 18PECh. 13.3 - Prob. 19PECh. 13.3 - Prob. 20PECh. 13.3 - Prob. 21PECh. 13.3 - Prob. 22PECh. 13.3 - Prob. 23PECh. 13.3 - Prob. 24PECh. 13.3 - Prob. 25PECh. 13.3 - Prob. 26PECh. 13.3 - Prob. 27PECh. 13.3 - Prob. 28PECh. 13.3 - Prob. 29PECh. 13.3 - Prob. 30PECh. 13.3 - Prob. 31PECh. 13.3 - Prob. 32PECh. 13.3 - For Exercises 33–40, use the equation in standard...Ch. 13.3 - Prob. 34PECh. 13.3 - Prob. 35PECh. 13.3 - Prob. 36PECh. 13.3 - Prob. 37PECh. 13.3 - Prob. 38PECh. 13.3 - Prob. 39PECh. 13.3 - Prob. 40PECh. 13.3 - Prob. 41PECh. 13.3 - Prob. 42PECh. 13.3 - Prob. 43PECh. 13.3 - Prob. 44PECh. 13.3 - Prob. 45PECh. 13.3 - Prob. 46PECh. 13.3 - Prob. 47PECh. 13.3 - Prob. 48PECh. 13.3 - Prob. 49PECh. 13.3 - Prob. 50PECh. 13.3 - Prob. 51PECh. 13.3 - Prob. 52PECh. 13.3 - Prob. 1PRECh. 13.3 - For Exercises 1–8, identify the formula. x 2 a 2 +...Ch. 13.3 - Prob. 3PRECh. 13.3 - Prob. 4PRECh. 13.3 - Prob. 5PRECh. 13.3 - Prob. 6PRECh. 13.3 - Prob. 7PRECh. 13.3 - Prob. 8PRECh. 13.3 - Prob. 9PRECh. 13.3 - Prob. 10PRECh. 13.3 - Prob. 11PRECh. 13.3 - Prob. 12PRECh. 13.3 - Prob. 13PRECh. 13.3 - Prob. 14PRECh. 13.3 - Prob. 15PRECh. 13.3 - Prob. 16PRECh. 13.3 - Prob. 17PRECh. 13.3 - Prob. 18PRECh. 13.3 - Prob. 19PRECh. 13.3 - Prob. 20PRECh. 13.3 - Prob. 21PRECh. 13.3 - Prob. 22PRECh. 13.3 - Prob. 23PRECh. 13.3 - Prob. 24PRECh. 13.3 - Prob. 25PRECh. 13.3 - Prob. 26PRECh. 13.3 - Prob. 27PRECh. 13.3 - Prob. 28PRECh. 13.3 - Prob. 29PRECh. 13.3 - Prob. 30PRECh. 13.4 - Given the system 2 x + y = 5 x 2 + y 2 = 50 Solve...Ch. 13.4 - Prob. 2SPCh. 13.4 - Prob. 3SPCh. 13.4 - Prob. 4SPCh. 13.4 - Solve the system by using the substitution method....Ch. 13.4 - Prob. 6SPCh. 13.4 - 1. a. A _______ system of equations in two...Ch. 13.4 - Prob. 2PECh. 13.4 - Prob. 3PECh. 13.4 - Prob. 4PECh. 13.4 - Prob. 5PECh. 13.4 - Prob. 6PECh. 13.4 - Prob. 7PECh. 13.4 - Prob. 8PECh. 13.4 - For Exercises 17–22, sketch each system of...Ch. 13.4 - Prob. 10PECh. 13.4 - Prob. 11PECh. 13.4 - Prob. 12PECh. 13.4 - Prob. 13PECh. 13.4 - Prob. 14PECh. 13.4 - Prob. 15PECh. 13.4 - Prob. 16PECh. 13.4 - Prob. 17PECh. 13.4 - Prob. 18PECh. 13.4 - Prob. 19PECh. 13.4 - Prob. 20PECh. 13.4 - Prob. 21PECh. 13.4 - Prob. 22PECh. 13.4 - Prob. 23PECh. 13.4 - Prob. 24PECh. 13.4 - Prob. 25PECh. 13.4 - Prob. 26PECh. 13.4 - Prob. 27PECh. 13.4 - Prob. 28PECh. 13.4 - Prob. 29PECh. 13.4 - For Exercises 32–48, solve the system of nonlinear...Ch. 13.4 - For Exercises 32–48, solve the system of nonlinear...Ch. 13.4 - Prob. 32PECh. 13.4 - Prob. 33PECh. 13.4 - Prob. 34PECh. 13.4 - Prob. 35PECh. 13.4 - Prob. 36PECh. 13.4 - Prob. 37PECh. 13.4 - Prob. 38PECh. 13.4 - Prob. 39PECh. 13.4 - For Exercises 32–48, solve the system of nonlinear...Ch. 13.4 - Prob. 41PECh. 13.4 - Prob. 42PECh. 13.4 - Prob. 43PECh. 13.4 - Prob. 44PECh. 13.4 - Prob. 45PECh. 13.4 - Prob. 46PECh. 13.4 - Prob. 47PECh. 13.4 - Prob. 48PECh. 13.4 - Prob. 49PECh. 13.4 - Prob. 50PECh. 13.5 - Graph the solution set of the inequality. x 2 + y...Ch. 13.5 - Prob. 2SPCh. 13.5 - Prob. 3SPCh. 13.5 - Prob. 4SPCh. 13.5 - Prob. 1PECh. 13.5 - Prob. 2PECh. 13.5 - Prob. 3PECh. 13.5 - Prob. 4PECh. 13.5 - a. Graph the solution set for x 2 + y 2 ≤ 9 . b....Ch. 13.5 - a. Graph the solution set for x 2 4 + y 2 9 ≥ 1....Ch. 13.5 - 19. a. Graph the solution set for.
b. How would...Ch. 13.5 - 20. a. Graph the solution set for
b. How...Ch. 13.5 - Prob. 9PECh. 13.5 - 22. A coordinate system is placed at the center of...Ch. 13.5 - For Exercises 23–37, graph the solution set. (See...Ch. 13.5 - For Exercises 23–37, graph the solution set. (See...Ch. 13.5 - Prob. 13PECh. 13.5 - For Exercises 23–37, graph the solution set. (See...Ch. 13.5 - Prob. 15PECh. 13.5 - Prob. 16PECh. 13.5 - Prob. 17PECh. 13.5 - Prob. 18PECh. 13.5 - Prob. 19PECh. 13.5 - Prob. 20PECh. 13.5 - Prob. 21PECh. 13.5 - Prob. 22PECh. 13.5 - For Exercises 23–37, graph the solution set. (See...Ch. 13.5 - For Exercises 23–37, graph the solution set. (See...Ch. 13.5 - Prob. 25PECh. 13.5 - For Exercises 38–51, graph the solution set to the...Ch. 13.5 - Prob. 27PECh. 13.5 - Prob. 28PECh. 13.5 - Prob. 29PECh. 13.5 - Prob. 30PECh. 13.5 - Prob. 31PECh. 13.5 - Prob. 32PECh. 13.5 - Prob. 33PECh. 13.5 - Prob. 34PECh. 13.5 - Prob. 35PECh. 13.5 - Prob. 36PECh. 13.5 - Prob. 37PECh. 13.5 - Prob. 38PECh. 13.5 - Prob. 39PECh. 13.5 - Prob. 40PECh. 13.5 - Prob. 41PECh. 13.5 - Prob. 42PECh. 13.5 - Prob. 43PECh. 13 - For Exercises 1-2, find the distance between the...Ch. 13 - For Exercises 1-2, find the distance between the...Ch. 13 - Find x such that ( x , 5 ) is 5 units from ( 2 , 9...Ch. 13 - 4. Find x such that is 3 units from
Ch. 13 - Prob. 5RECh. 13 - For Exercises 5–8, find the center and the radius...Ch. 13 - Prob. 7RECh. 13 - For Exercises 5–8, find the center and the radius...Ch. 13 - Prob. 9RECh. 13 - For Exercises 10–13, write the equation of the...Ch. 13 - Prob. 11RECh. 13 - Prob. 12RECh. 13 - Prob. 13RECh. 13 - Prob. 14RECh. 13 - Prob. 15RECh. 13 - For Exercises 16–17, find the midpoint of the...Ch. 13 - For Exercises 16–17, find the midpoint of the...Ch. 13 - For Exercises 18–21, determine whether the axis of...Ch. 13 - For Exercises 18–21, determine whether the axis of...Ch. 13 - For Exercises 18–21, determine whether the axis of...Ch. 13 - For Exercises 18–21, determine whether the axis of...Ch. 13 - For Exercises 22–25, determine the coordinates of...Ch. 13 - For Exercises 22–25, determine the coordinates of...Ch. 13 - For Exercises 22–25, determine the coordinates of...Ch. 13 - For Exercises 22–25, determine the coordinates of...Ch. 13 - For Exercises 26–29, write the equation in...Ch. 13 - For Exercises 26–29, write the equation in...Ch. 13 - For Exercises 26–29, write the equation in...Ch. 13 - For Exercises 26–29, write the equation in...Ch. 13 - For Exercises 30–31, identify the x- and...Ch. 13 - For Exercises 30–31, identify the x- and...Ch. 13 - For Exercises 32–33, identify the center of the...Ch. 13 - For Exercises 32–33, identify the center of the...Ch. 13 - For Exercises 34–37, determine whether the...Ch. 13 - For Exercises 34–37, determine whether the...Ch. 13 - For Exercises 34–37, determine whether the...Ch. 13 - For Exercises 34–37, determine whether the...Ch. 13 - For Exercises 38–39, graph the hyperbola by first...Ch. 13 - For Exercises 38–39, graph the hyperbola by first...Ch. 13 - For Exercises 40–43, identify the equations as...Ch. 13 - For Exercises 40–43, identify the equations as...Ch. 13 - For Exercises 40–43, identify the equations as...Ch. 13 - For Exercises 40–43, identify the equations as...Ch. 13 - For Exercises 44–47, a. Identify each equation as...Ch. 13 - For Exercises 44–47,
a. Identify each equation as...Ch. 13 - For Exercises 44–47, a. Identify each equation as...Ch. 13 - For Exercises 44–47,
a. Identify each equation as...Ch. 13 - For Exercises 48–53, solve the system of nonlinear...Ch. 13 - For Exercises 48–53, solve the system of nonlinear...Ch. 13 - For Exercises 48–53, solve the system of nonlinear...Ch. 13 - For Exercises 48–53, solve the system of nonlinear...Ch. 13 - For Exercises 48–53, solve the system of nonlinear...Ch. 13 - For Exercises 48–53, solve the system of nonlinear...Ch. 13 - For Exercises 54–59, graph the solution set to the...Ch. 13 - For Exercises 54–59, graph the solution set to the...Ch. 13 - For Exercises 54–59, graph the solution set to the...Ch. 13 - For Exercises 54–59, graph the solution set to the...Ch. 13 - For Exercises 54–59, graph the solution set to the...Ch. 13 - For Exercises 54–59, graph the solution set to the...Ch. 13 - For Exercises 60–61, graph the solution set to the...Ch. 13 - For Exercises 60–61, graph the solution set to the...Ch. 13 - 1. Use the distance formula to find the distance...Ch. 13 - Prob. 2TCh. 13 - Prob. 3TCh. 13 - Prob. 4TCh. 13 - 5. Find the center of the circle that has a...Ch. 13 - Determine the vertex and the equation of the axis...Ch. 13 - Write the equation in standard form y = a ( x − h...Ch. 13 - 8. Graph the ellipse.
Ch. 13 - 9. Graph the ellipse.
Ch. 13 - Graph the hyperbola. y 2 − x 2 4 = 1Ch. 13 - For Exercises 11–12, solve the system and identify...Ch. 13 - For Exercises 11–12, solve the system and identify...Ch. 13 - Describe the circumstances in which a nonlinear...Ch. 13 - 14. Solve the system by using either the...Ch. 13 - For Exercises 15–18, graph the solution...Ch. 13 - For Exercises 15–18, graph the solution...Ch. 13 - For Exercises 15–18, graph the solution set. x < y...Ch. 13 - For Exercises 15–18, graph the solution set. y < x...
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- In Exercises 11–16, find the vertex, focus, and directrix of the parabola, and sketch its graph.arrow_forwardIn Exercises 35–42, find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola. 35. (x – 2) = 8(y – 1) 37. (x + 1) = -8(y + 1) 39. (y + 3) = 12(x + 1) 41. (y + 1) = -&r 36. (x + 2) = 4(y + 1) 38. (x + 2) = -8(y + 2) 40. (y + 4)2 = 12(x + 2) %3D %3D 42. (y - 1) = -&rarrow_forwardIn Exercises 3–16, find the coordinates of the vertices and foci of the given ellipses. Sketch each curve.arrow_forward
- Write the equation of the ellipse that has a center at (- 4, - 5), a focus at ( – 1, – 5), and a vertex at (- 8, - 5). |arrow_forwardIn Exercises 3–10, describe the curve represented by each equation. Identify the type of curve and its center (or vertex if it is a parabola). Sketch each curve.arrow_forwardFor Exercises 79–82, write the standard form of an equation of the ellipse subject to the following conditions. 79. Center: (0, 0); Eccentricity: ; Major axis vertical of length 34 units 80. Center: (0, 0); Eccentricity: ; Major axis vertical of length 82 units 81. Foci: (0, – 1) and (8, – 1); Eccentricity: 82. Foci: (0, – 1) and (-6, –1); Eccentricity:arrow_forward
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