Math Chapter 10 Test Review

Pre-Calculus Chapter 10 Conics Review Name ___________________________ March 2015 Graph the ellipse and identify the center, vertices, and foci. 1. 𝑥2 9 𝑦2 2. 4𝑥 2 + 25𝑦 2 = 100 + 25 = 1 Center:___________ Center:___________ Vert:____________ Vert:____________ Foci:____________ Foci:____________ 3. 𝑥 2 + 4𝑦 2 = 36 4. 𝑥 2 + Center:___________ Center:___________ Vert:____________ Vert:____________ Foci:____________ Foci:____________ 5. (𝑥 − 1)2 4 + (𝑦 + 2)2 9 =1 𝑦2 4 =1 6. 36(𝑥 + 4)2 + (𝑦 + 3)2 = 36 Center:___________ Center:___________ Vert:____________ Vert:____________ Foci:____________ Foci:____________ Find the standard form of the equation of each ellipse. 7. Foci (0, ± 3), vertices (0, ± 5) 8. Major axis horizontal with length 12; length of minor axis 4; center: (- 1, 3) 9. Foci (± 5, 0), length of major axis 12 10. Endpoints of major axis: (2, 2) & (8, 2) Endpoints of minor axis: (5, 3) & (5, 1) 11. 12. Convert each equation to standard form by completing the square. 13. 4𝑥 2 + 36𝑦 − 32𝑥 + 9𝑦 2 + 64 = 0 14. 9𝑥 2 + 16𝑦 2 − 18𝑥 + 64𝑦 − 71 = 0 Graph the hyperbola and identify the center, vertices, asymptotes, and foci. 15. 𝑦2 9 𝑥2 16. 4𝑥 2 − 𝑦 2 = 16 − 16 = 1 Center: ___________ Center: ___________ Vertices:___________ Vertices:___________ Foci:__________ Foci:__________ Asymptotes:________ Asymptotes:________ 17. 4(𝑥 − 1)2 − 9(𝑦 + 2)2 = 36 18. Center:____________ Center: ____________ Vertices:___________ Vertices:___________ Foci:__________ Foci:__________ Asymptotes:________ Asymptotes:________ 19. (𝑦 + 2)2 25 − (𝑥 − 3)2 16 =1 20. (𝑦 + 1)2 25 (𝑥 − 2)2 25 − – (𝑥 − 2)2 =1 9 (𝑦 + 3)2 16 =1 Center: ___________ Center: ___________ Vertices:___________ Vertices:___________ Foci:__________ Foci:__________ Asymptotes:________ Asymptotes:________ Find the standard form of the equation of each hyperbola. 21. Foci (0, ± 4), vertices (0, ± 2) 22. Vertices (± 4, 0), Asymptotes: 𝑦 = ± 3𝑥 23. Endpoints of transverse axis: (0, ± 6) Asymptotes: y = ± 2x 24. Foci (0, ± 1), length of transverse axis 1 25. 26. 𝒚 = 𝟑𝒙 𝒚 = − 𝟑𝒙 Convert each equation to standard form by completing the square. 27. 4𝑥 2 − 𝑦 2 + 32𝑥 + 6𝑦 + 39 = 0 28. 9𝑦 2 − 4𝑥 2 − 18𝑦 + 24𝑥 − 63 = 0 Graph the parabola and identify the vertex, directrix, and focus. 29. 𝑦 2 = −12𝑥 30. 𝑥 2 = 8𝑦 Vertex: _______ Vertex: _______ Dir: _______ Dir: ____________ Focus: ___________ Focus:_________ 31. 6(𝑥 + 1)2 + 12(𝑦 − 3) = 0 32. 𝑦 2 − 12(𝑥 + 2) = 0 Vertex: _______ Vertex: _______ Dir: ___________ Dir: __________ Focus: ________ Focus:________ 33. (𝑥 + 2)2 = −8(𝑦 + 2) 34. (𝑦 − 1)2 = −8𝑥 Vertex: _______ Vertex: _______ Dir: _______ Dir: ____________ Focus: ___________ Focus:_________ Write an equation in standard form for the parabola satisfying the given conditions. 35. Focus: (9, 0); Directrix: x = -9 36. Focus: (-10, 0); Directrix: x = 10 37. Vertex: (5, -2); Focus (7, -2) 38. Focus: (2, 4); Directrix: x = -4 Find the equation for the parabola whose graph is shown. 39. 40. F(0, -3) Convert each equation to standard form by completing the square. 41. 𝑥 2 + 6𝑥 + 8𝑦 + 1 = 0 42. 𝑦 2 + 8𝑦 − 4𝑥 + 8 = 0 Answers: 1. 𝐶(0, 0); 𝑉(0, ± 5); 𝐹(0, ± 4) 2. 𝐶(0, 0); 𝑉(± 5, 0); 𝐹(± √21, 0) 3. 𝐶(0, 0); 𝑉(± 6, 0); 𝐹(± 3√3, 0) 4. 𝐶(0, 0); 𝑉(0, ± 2); 𝐹(0, ± √3) 5. 𝐶(1, −2); 𝑉(1, 1); (1, −5); 𝐹(1, − 2 ± √5) 6. 𝐶(−4, −3); 𝑉(−4, 3); (−4, −9); 𝐹(−4, − 3 ± √35) 7. 𝑥2 𝑦2 + 25 = 1 16 11. 𝑥2 9 8. 𝑦2 + 25 = 1 (𝑥 + 1)2 36 12. + (𝑥 + 3)2 4 (𝑦 − 3)2 4 + =1 (𝑦 − 2)2 1 9. =1 3 15. 𝐶(0, 0); 𝑉(0, ± 3); 𝐹(0, ± 5); 𝑇: 𝑦 = ± 4 𝑥 𝑥2 𝑦2 + 11 = 1 36 13. (𝑥 − 4)2 9 + 10. (𝑦 + 2)2 =1 4 14. (𝑥 − 5)2 9 (𝑥 − 1)2 16 + + (𝑦 − 2)2 1 (𝑦 + 2)2 9 =1 =1 16. 𝐶(0, 0); 𝑉(± 2, 0); 𝐹(± 2√5, 0); 𝑇: 𝑦 = ± 2𝑥 2 17. 𝐶(1, −2); 𝑉(−2, −2) ; (4, −2); 𝐹(1 ± √13 , − 2); 𝑇: 𝑦 + 2 = ± 3 (𝑥 − 1) 5 18. 𝐶(2, −1); 𝑉(2, 4) ; (2, −6); 𝐹(2, − 1 ± √34); 𝑇: 𝑦 + 1 = ± 3 (𝑥 − 2) 5 19. 𝐶(3, −2); 𝑉(3, 3) ; (3, −7); 𝐹(3, − 2 ± √41); 𝑇: 𝑦 + 2 = ± 4 (𝑥 − 3) 4 20. 𝐶(2, −3); 𝑉(−3, −3) ; (7, −3); 𝐹(2 ± √41, −3); 𝑇: 𝑦 + 3 = ± 5 (𝑥 − 2) 21. 25. 𝑦2 4 𝑥2 − 12 = 1 (𝑥 − 2)2 4 − 22. (𝑦 − 1)2 9 =1 26. 𝑥2 𝑦2 − 144 = 1 16 𝑦2 9 − 𝑥2 1 29. 𝑉(0, 0); Dir: 𝑥 = 3; 𝐹(−3, 0) 31. 𝑉(−1, 3); Dir: 𝑦 = 7 5 ; 𝐹(−1, 2) 2 =1 23. 27. 𝑦2 − 36 𝑥2 9 (𝑥 + 4)2 4 =1 − 24. (𝑦 − 3)2 16 =1 28. 𝑦2 1⁄ 4 𝑥2 − 3⁄ = 1 4 (𝑦 − 1)2 4 − (𝑥 − 3)2 9 30. 𝑉(0, 0); Dir: 𝑦 = − 2; 𝐹(0, 2) 32. 𝑉(−2, 0); Dir: 𝑥 = − 5; 𝐹(1, 0) 33. 𝑉(−2, −2); Dir: 𝑦 = 0; 𝐹(−2, −4) 34. 𝑉(0, 1); Dir: 𝑥 = 2; 𝐹(−2, 1) 35. 𝑦 2 = 36𝑥 36. 𝑦 2 = −40𝑥 37. (𝑦 + 2)2 = 8(𝑥 − 5) 38. (𝑦 − 4)2 = 12(𝑥 + 1) 39. 𝑦 2 = 8𝑥 40. 𝑥 2 = −12𝑦 41. (𝑥 + 3)2 = −8(𝑦 − 1) 42. (𝑦 + 4)2 = 4(𝑥 + 2) =1