Math Chapter 9 Test Review Answers

Algebra 2 CP Name________________ Date_________________ Find the midpoint and distance between each pair of points whose coordinates are given. Express answers in simplest form. 1. (-2, -4) and (3, 4) 2. (2, -5) and (-3, -1) 3. (5, 2) and (-1, 4) Midpoint ___________ Midpoint ___________ Midpoint ___________ Distance ___________ Distance ___________ Distance ___________ Graph the circle. Identify the center and radius. 4. 5. 4.______________ Center ________________ Radius 5.______________ Center ________________ Radius Write the equation of the circle that satisfies the given information. 6. Center (0, 0) r = 9 7. Center (4, -2) 8. Center (0, 0) and the point on the circle (-3, 5) 9. Center (1, 7) and the point on the circle (4, -6) Graph the ellipse. Identify the vertices, co-vertices, and foci of the ellipse. 10. 11. 10._____________ Vertices ________________ Co-Vertices ________________ Foci 11._____________ Vertices ________________ Co-Vertices ________________ Foci 12. 13. 12._____________ Vertices ________________ Co-Vertices ________________ Foci 13._____________ Vertices ________________ Co-Vertices ________________ Foci Find the coordinates of the foci of the ellipse centered at the origin with the given information. 14. Vertices: (0, -4) (0, 4); 15. Vertices: (-3, 0) (3, 0); Co-vertices: (-2, 0) (2, 0) Co-vertices: (0, -1) (0, 1) Write an equation of an ellipse that satisfies the given information. 16. Center (2, 1); Vertex (2, -6); 17. Center (0, 0); Vertex (7, 0); Co-Vertex (4, 1) Co-Vertex (0, 3) 18. Center (-1, 1); Vertex (-1, -8); Focus (-1, -6) 19. Vertices: (0, 3) (8, 3); Foci: (1, 3) (7, 3) Graph the parabola. Label the focus, directrix, and axis of symmetry. 20. 21. Vertex:_______________ Vertex:_______________ Focus:_______________ Focus:_______________ Directrix:_____________ Directrix:_____________ Axis of Symmetry:______ Axis of Symmetry:______ Write the equation of the parabola with the given conditions. 22. Vertex: (2, 1) 24. Vertex: (-3, -2) Focus: (5, 1) Directrix: y = - 5 23. Vertex: (0, 0) Focus: 25. Vertex: (0, 0) Directrix: x = 6 Identify the vertices and foci of the hyperbola. 26. 27. Graph the hyperbola. Identify the asymptotes, vertices, and foci. 28. 29. 28._____________ Asymptotes ________________ Vertices ________________ Foci 29._____________ Asymptotes ________________ Vertices ________________ Foci 30. 30._____________ Asymptotes ________________ Vertices ________________ Foci Write an equation of a hyperbola that satisfies the given conditions. 31. Foci (-7, 0) (7, 0) 32. Foci (0, -5) (0, 5) Vertices (-4, 0) (4, 0) Vertices (0, -3) (0, 3) 33. Foci (6, -6) (6, 4) Vertices (6, -3) (6, 1) 34. Foci (-9, 3) (1, 3) Vertices (-7, 3) (-1, 3) Identify the conic section from its equation. A) For circles, also identify the radius B) For ellipses, also identify the vertices, co-vertices, and foci C) For parabolas, also identify the axis of symmetry, focus, and directrix D) For hyperbolas, also identify the vertices and foci 35. 36. 37. 38. 39. 40. ANSWERS 1. MP: (1/2, 0); D: 2. MP: (-1/2, -3); D: 4. C: (0, 0); r = 3 5. CP: (2, -1); r = 7. 3. 6. 8. 10. V: (0, ±5); CV: (±3, 0); F: (0, ±4) 9. 11. V: (4, -3) (-8, -3); CV: (-2, -0.2) (-2, -5.8); F: (3.3, -3) (-7.3, -3) 12. V: (1, 1.6) (1, -3.6); CV: (0, -1) (2, -1); F: (1, 1.4) (1, -3.4) 14. MP: (2, 3); D: 15. 13. V: (±5, 0); CV: 16. 18. ; F: 17. 19. 20. V: (0, 0); F: (9/8, 0); D: x = -9/8; x-axis 21. V: (1, -2); F: (1, -4); D: y = 0, y-axis 22. 23. 24. 26. V: (±4, 0); F: 27. V: (0, ±2); F: 25. 28. Asy: ; V: (±7, 0); F: 29. Slope: ±1/2; V: (-3, 4) (-3, -2); F: (-3, 7.7) (-3, -5.7) 30. Asy: y = ±2x, V: (±1, 0); F: 31. 33. 32. 34. 35. Parabola; V: (3, 1); x-axis; F: (6, 1); D: x = 0 36. Circle; C: (1, -3); r = 1 37. Parabola; V: (0, -1); y-axis; F: (0, 1.25); D: y = -3.25 38. Circle; C: (0, -2); 39. Hyperbola; C: (-1, 2); V: (-2, 2) (0, 2); F: (-6.1, 2) (4.1, 2) x y 40. Ellipse; V: (-2, 0) (6, 0); CV: (2, 1) (2, -1); F: (-1.9, 0) (5.9, 0)