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Ch. 9 – Conics Study Guide ____ Graph: 1. Find the focus of the parabola: a. (–3, 0) c. (0, –3) b. (0, 3) d. (3, 0) 2. Sketch the graph of the equation 14. . 3. Identify the focus and the directrix of the parabola given by 4. Write the standard form of the equation of the parabola with its vertex at (0, 0) and focus at . 15. 16. Find the vertices and the foci of the hyperbola. 17. Write the equation of the hyperbola with vertices at and foci at Graph: 5. 18. Find the equation of the circle with center (2, –6) and radius of 4. 6. 7. Write the standard form of the equation of the circle that passes through the point (0, 1) with its center at the origin. 8. Write the standard form of the equation of the circle that passes through the point (3, 4) with its center at the origin. ____ 19. Find the center and radius of a. center (1, –5); r = 16 c. center (–1, 5); r = 16 b. center (1, –5); r = 4 d. center (–1, 5); r = 4 20. Write the equation of the circle in standard form. Identify the radius and center. Graph: 9. 21. Classify the conic section as a circle, an ellipse, a hyperbola, or a parabola. 10. 11. Determine the foci and vertices of the graph of 22. Classify the conic section as a circle, an ellipse, a hyperbola, or a parabola. . 12. Write an equation of the ellipse with a vertex at (9, 0), a co-vertex at (0, 5), and center at (0, 0). 13. Write an equation of the ellipse with a vertex at (5, 0), a focus at (4, 0), and center at (0, 0). 23. Classify the conic section as a circle, an ellipse, a hyperbola, or a parabola. Sketch the graph: 24. Ch. 9 – Conics Study Guide 25. Find an equation of the hyperbola with vertices at (–3, 2) and (3, 2) and foci at (–5, 2), (5, 2). 26. Find an equation of the parabola with vertex at (– 3, 1) and focus (–1, 1). 27. Write the equation in standard form and classify the conic section. 28. Find an equation of the ellipse with vertices at (– 2, 2) and (4, 2), and co-vertices at (1, 4) and (1, 0). ____ 29. Classify the conic section as a circle, an ellipse, a hyperbola, or a parabola. a. parabola b. hyperbola c. circle d. ellipse 30. Write the equation in standard form, then sketch the graph of the equation. 31. Find the points of intersection, if any, of the graphs in the system. 32. Find the points of intersection, if any, of the graphs in the system. Solve: ____ 33. a. {(0, 0), (3, )} b. (3, ), ( , )} c. {(0, ), ( , 0)} d. {(0, 3), (3, 0)} Ch. 9 – Conics Study Guide Ch. 9 Test Answer Section 1. ANS: D 2. ANS: 16. ANS: DIF: Vertices: DIF: DIF: Level A Level B Level B Foci: 17. ANS: DIF: Level B y 10 18. ANS: 19. ANS: D 20. ANS: –10 10 DIF: Directrix: DIF: DIF: Level B Level B Center: (2, –3) Radius: 2 x –10 3. ANS: DIF: Level B Level B 21. ANS: Hyperbola 22. ANS: Parabola 23. ANS: Ellipse 24. ANS: DIF: DIF: DIF: DIF: Level B Level B Level B Level B Focus: 4. ANS: 5. ANS: DIF: DIF: Level B Level B y 10 10 x –10 –10 6. 7. 8. 9. 10. 11. ANS: C ANS: ANS: ANS: B ANS: C ANS: vertices = DIF: DIF: DIF: DIF: DIF: DIF: ; foci = (0, Level A Level B Level B Level A Level A Level B 33 ) 12. ANS: DIF: Level B 13. ANS: DIF: Level B 14. ANS: DIF: Level B 15. ANS: C DIF: Level B 25. ANS: DIF: Level B 26. ANS: DIF: Level B (Forms may vary.) 27. ANS: DIF: Level B ; The figure is an ellipse. 28. ANS: 29. ANS: B 30. ANS: DIF: Level B DIF: DIF: Level B Level B 31. ANS: (0, 0), (–4, 4) 32. ANS: , DIF: Level A DIF: Level A 33. ANS: D Level B DIF: