University:
Carleton College
Course:
MATH 111 | Introduction to Calculus
Academic year:

2024
Views:

149

Pages:

6
Author:

Clint W.

Pre-Calculus Ellipses HW Day 1 Graph the ellipse and identify the center, vertices, and foci. 1. x²/16 + y²/4 = 1 Center: (0, 0) Vertices: (±4, 0) Co-vertices: (0, ±2) Foci: (±2√3, 0) 2. x²/9 + y²/36 = 1 Center: (0, 0) Vertices: (0, ±6) Co-vertices: (±3, 0) Foci: (0, ±3√3) 3. 25x² + 4y² = 100 Center: (0, 0) Vertices: (0, ±5) Co-vertices: (±2, 0) Foci: (0, ±√21) 4. 7x² = 35 - 5y² Center: (0, 0) Vertices: (0, ±√7) Co-vertices: (±√5, 0) Foci: (0, ±√2) 5. (x-2)²/9 + (y+1)²/4 = 1 Center: (2, -1) Vertices: (5, -1), (-1, -1) Co-vertices: (2, 1), (2, -3) Foci: (2±√5, -1) 6. (x-4)²/9 + (y+2)²/25 = 1 Center: (4, -2) Vertices: (4, 3), (4, -7) Co-vertices: (1, -2), (7, -2) Foci: (4, 2), (4, -6) 7. (x+3)² + 4(y-2)² = 16 Center: (-3, 2) Vertices: (1, 2), (-7, 2) Co-vertices: (-3, 4), (-3, 0) Foci: (-3 ± 2√3, 2) 8. x²/25 + (y-2)²/36 = 1 Center: (0, 2) Vertices: (0, 8), (0, -4) Co-vertices: (5, 2), (-5, 2) Foci: (0, 2 ± √11) Find the standard form of the equation of each ellipse. 9. (x²/9) + (y²/1) = 1 10. (x²/9) + (y²/25) = 1 11. (x+1)²/4 + y²/1 = 1 Find the standard form of the equation of each ellipse satisfying the given conditions. 12. Foci: (±5, 0); Vertices (±8, 0) (x²/64) + (y²/39) = 1 13. Foci: (0, ±4); Vertices: (0, ±7) (x²/33) + (y²/49) = 1 14. Foci: (±2, 0); y-intercepts: ±3 (x²/13) + (y²/9) = 1 15. Major axis horizontal with length 8; length of minor axis 4; Center (0, 0) (x²/16) + (y²/4) = 1 Pre-Calculus Ellipses HW Day 2 Name: Graph the ellipse and identify the center, vertices, and foci. 1. x²/25 + y²/9 = 1 Center: (0, 0) Vertices: (0, ±5) Co-vertices: (±3, 0) Foci: (0, ±4) 2. x² + 4y² = 4 x²/4 + y²/1 = 1 Center: (0, 0) Vertices: (±2, 0) Co-vertices: (0, ±1) Foci: (±√3, 0) 3. (x+3)²/9 + (y-2)² = 1 Center: (-3, 2) Vertices: (0, 2), (-6, 2) Co-vertices: (-3, 5), (-3, -1) Foci: (-3±2√2, 2) 4. 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)