Name: _______________________________________________ Period: __________ Date: ______________ID: A
Algebra 2 Chapter 10 Practice Test All work is to be completed on a separate sheet of paper for full credit! 9. Write an equation in standard form for the circle.
1. Graph the equation. Identify the vertices, co-vertices, and foci. 16x 2 + 4y 2 = 49 2. Graph the equation. Identify the vertices, co-vertices, and foci. x2 + y2 = 9 3. Graph the equation.Identify the vertices, foci and asymptotes. x 2 − y 2 = 64 4. Write an equation for the translation of x 2 + y 2 = 25 , 2 units right and 4 units down. 5. Write an equation for the graph.
10. Write an equation of a circle with center (–5, –8) and radius 2. 11. Write an equation in standard form of an ellipse that has a vertex at (5, 0), a co-vertex at (0, –3), and is centered at the origin. 12. Graph the conic section. 4x 2 − 9y 2 = 144 13. Write an equation of an ellipse in standard form with the center at the origin and with the given characteristics. height of 12 units and width of 19 units 6. Write an equation of an ellipse in standard form with the center at the origin and with the given characteristics. vertices at (–5, 0) and co-vertices (0, 4)
14. Write an equation of a hyperbola with vertices (3, –2) and (–9, –2), and foci (7, –2) and (–13, –2). 15. A satellite is launched in a circular orbit around Earth at an altitude of 120 miles above the surface. The diameter of Earth is 7920 miles. Write an equation for the orbit of the satellite if the center of the orbit is the center of the Earth labeled (0, 0).
7. Find the foci of the graph 25x 2 − 36y 2 − 900 = 0. Draw the graph. 8. Write an equation of an ellipse with center (3, –3), vertical major axis of length 12, and minor axis of length 6.
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ID: A 16. Find the center and radius of the circle with 2 2 equation (x − 5 ) + ÁÊË y + 6 ˜ˆ¯ = 9.
24. Find the center and radius of the circle with equation (x − 1) 2 + (y + 1) 2 = 4. 25. Write the equation of a circle with center (8, 7) and radius r = 6.
17. Find the foci of the ellipse with the equation y2 x2 + = 1. Graph the ellipse. 49 64
26. Graph the ellipse 18. This ellipse is being used for a design on a poster. Name the vertices and co-vertices of the graph. Find the foci.
(x − 6) 2 (y + 5) 2 + = 1. 100 64
27. Find the vertices, co-vertices, and asymptotes of the (y − 1) 2 (x + 2 ) 2 − = 1, and then graph. hyperbola 25 9 28. Write an equation of a hyperbola with vertices (1, 3) and (–5, 3), and foci (3, 3) and (–7, 3). 29. Write an equation of an ellipse with center (3, 2), vertical major axis of length 12, and minor axis of length 6. 30. Write the equation of the circle 2 2 (x − 5 ) + ÊÁË y + 3 ˆ˜¯ = 4, translated 3 units right and 5 units up. 31. Find the vertices and asymptotes of 16x 2 − 25y 2 = 400.
19. An elliptical track has a major axis that is 48 yards long and a minor axis that is 34 yards long. Find an equation for the track if its center is (0, 0) and the major axis is the x-axis.
32. Write an equation of the ellipse with center at the origin and focus ÊÁË 0,3 ˆ˜¯ , y-intercept 5
20. Write an equation of an ellipse with center (3, 4), horizontal major axis of length 16, and minor axis of length 10. 21. Write an equation for an ellipse with center (1, –3), vertices (1, 2) and (1, –8), and co–vertices (4, –3) and (–2, –3). 22. Write an equation of the ellipse with foci at (0, ±11) and vertices at (0, ±12). Graph the ellipse. 23. Find the equation of a hyperbola with a = 452 units and c = 765 units. Assume that the transverse axis is horizontal.
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ID: A
Algebra 2 Chapter 10 Practice Test Answer Section SHORT ANSWER 1. ANS: The graph is an ellipse. The center is at the origin. It has two lines of symmetry,
the x-axis and the y-axis.
REF: 10-1 Exploring Conic Sections 2. ANS:
The graph is a circle of radius 3. Its center is at the origin. Every line through the center is a line of symmetry. REF: 10-1 Exploring Conic Sections
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ID: A 3. ANS:
The graph is a hyperbola that consists of two branches. Its center is at the origin. It has two lines of symmetry, the x-axis and the y-axis. REF: 10-1 Exploring Conic Sections 4. ANS: 2 2 (x − 2 ) + ÊÁË y + 4 ˆ˜¯ = 25 REF: 10-3 Circles 5. ANS: y2 x2 + = 1 4 16 REF: 10-4 Ellipses 6. ANS: y2 x2 + = 1 25 16 REF: 10-4 Ellipses
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ID: A 7. ANS: (− 61 , 0), (
61 , 0)
REF: 10-5 Hyperbolas 8. ANS: ÊÁ y + 3 ˆ˜ 2 2 (x − 3 ) Ë ¯ + = 1 9 36 REF: 10-6 Translating Conic Sections 9. ANS: 2 2 (x + 1 ) + ÊÁË y + 3 ˆ˜¯ = 4 REF: 10-3 Circles 10. ANS: 2 2 (x + 5 ) + ÁÊË y + 8 ˜ˆ¯ = 4 REF: 10-3 Circles 11. ANS: y2 x2 + = 1 25 9 REF: 10-4 Ellipses
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ID: A 12. ANS:
REF: 10-5 Hyperbolas 13. ANS: y2 x2 + = 1 90.25 36 REF: 10-4 Ellipses 14. ANS: ÊÁ y + 2 ˆ˜ 2 (x + 3) 2 Ë ¯ − = 1 36 64 REF: 10-6 Translating Conic Sections 15. ANS: x 2 + y 2 = 16, 646, 400 REF: 10-3 Circles 16. ANS: (5, –6); 3 REF: 10-3 Circles
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ID: A 17. ANS: foci (0, ±
15 )
REF: 10-4 Ellipses 18. ANS: (±7.5, 0), (0, ±5) REF: 10-1 Exploring Conic Sections 19. ANS: y2 x2 + = 1 576 289 REF: 10-4 Ellipses 20. ANS: ÊÁ y − 4 ˆ˜ 2 2 (x − 3 ) Ë ¯ + = 1 64 25 REF: 10-6 Translating Conic Sections 21. ANS: 2 2 ÁÊ y + 3 ˜ˆ (x − 1 ) Ë ¯ + = 1 9 25 REF: 10-6 Translating Conic Sections
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ID: A 22. ANS: y2 x2 + = 1 23 144
REF: 10-4 Ellipses 23. ANS: y2 x2 − = 1 204, 304 380, 921 REF: 10-5 Hyperbolas 24. ANS: center (1, –1); radius 2 REF: 10-3 Circles 25. ANS: 36 = (x − 8) 2 + (y − 7) 2 REF: Page 729
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ID: A 26. ANS:
REF: Page 738 27. ANS: Vertices: (−2, 6) and (−2, − 4) Co-vertices: (1, 1) and (−5, 1) Asymptotes: y − 1 =
5 3
5
(x + 2 ) and y − 1 = − 3 (x + 2 )
REF: Page 746 28. ANS: ÊÁ y − 3 ˜ˆ 2 (x + 2) 2 Ë ¯ − = 1 9 16 REF: 10-6 Translating Conic Sections 29. ANS: ÊÁ y − 2 ˆ˜ 2 2 (x − 3 ) Ë ¯ + = 1 9 36 REF: 10-6 Translating Conic Sections 7
ID: A 30. ANS: 2 2 (x − 8 ) + ÁÊË y + 2 ˜ˆ¯ = 4 31. ANS: ÊÁ ±5,0ˆ˜ ; y = ± 4 x Ë ¯ 5 32. ANS: 2 x2 y + =1 16 25
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