University:
Florida Gateway College
Course:
MAC 1140 | Precalculus
Academic year:

2019
Views:

471

Pages:

2
Author:

Clint W.

Ellipses (Day 2) WS Name: Graph the ellipse and identify the center, vertices, and foci. 1. (x+3)²/9 + (y-2)²/1 = 1 Center: (-3, 2) Vertices: (0, 2), (-6, 2) Co-vertices: (-3, 3), (-3, 1) Foci: (-3±2√2, 2) 2. 9(x-1)² + 4(y+3)² = 36 (x-1)²/4 + (y+3)²/9 = 1 Center: (1, -3) Vertices: (1, 0), (1, -6) Co-vertices: (3, -3), (-1, -3) Foci: (1, -3±√5) Find the standard form of the equation of each ellipse. 3. Horizontal a = 3, b = 1, h = 0, k = 0 x²/9 + y²/1 = 1 4. Horizontal a = 2, b = 1, h = -4, k = 4 (x+4)²/4 + (y-4)²/1 = 1 5. Vertical a = 5, b = 3, h = 5, k = -2 (x-5)²/9 + (y+2)²/25 = 1 6. Foci: (±5, 0); Vertices: (±8, 0) c = 5, a = 8, h = 0, k = 0 c² = a² - b² 25 = 64 - b² b² = 39 x²/64 + y²/39 = 1 7. Foci: (0, ±4); Vertices: (0, ±7) c = 4, a = 7, h = 0, k = 0 c² = a² - b² 16 = 49 - b² b² = 33 x²/33 + y²/49 = 1 8. Foci: (±2, 0); y-intercepts: ±3 c = 2, b = 3, h = 0, k = 0 c² = a² - b² 4 = a² - 9 a² = 13 x²/13 + y²/9 = 1 9. Major axis horizontal with length 8; length of minor axis 4; Center (0, 0) a = 4, b = 2, h = 0, k = 0 x²/16 + y²/4 = 1 Find the standard form of the equation of each ellipse satisfying the given conditions. 10. Major axis vertical with length 10; length of minor axis 4; Center: (-2,3) 2a = 10, a = 5 2b = 4, b = 2 (x+2)²/4 + (y-3)²/25 = 1 11. Endpoints of major axis: (7, 9) & (7, 3); Endpoints of minor axis: (5, 6) & (9, 6) 2a = 6, a = 3 2b = 4, b = 2 Center = (7, 6) (x-7)²/4 + (y-6)²/9 = 1 Convert each equation to standard form by completing the square. 12. 9x² + 25y² + 36x + 50y - 164 = 0 9(x² + 4x + 4) + 25(y² + 2y + 1) = 164 + 36 + 25 9(x+2)² + 25(y+1)² = 225 (x+2)²/25 + (y+1)²/9 = 1 13. x² + 4y² + 10x - 8y - 13 = 0 x² + 10x + 4y² - 8y = 13 (x+5)² + 4(y-1)² = 16 (x+5)²/16 + (y-1)²/4 = 1 14. 4x² + y² + 16x - 6y - 39 = 0 4(x² + 4x) + y² - 6y = 39 4(x+2)² + (y-3)² = 64 (x+2)²/16 + (y-3)²/64 = 1 15. 4x² + 25y² - 24x + 100y + 36 = 0 4(x² - 6x) + 25(y² + 4y) = -36 4(x-3)² + 25(y+2)² = 100 (x-3)²/25 + (y+2)²/4 = 1