Exercise Set 8.1: Classifying Conic Sections Describe how the coefficients (A, B, C, D, E, and F) of the terms of general conic equation, Ax 2 + By 2 + Cx + Dy + E + F = 0 , would result in the following conic. 1. Parabola 2. Circle 3. Ellipse 4. Hyperbola Classify each conic section as a circle, parabola, ellipse, or hyperbola. 5. x 2 + y 2 = 25 6. x 2 − y 2 = 25
15. x 2 − y 2 − 2x − 8 = 0 16. (x −1)2 +
y2 =1 25
7. x = y 2 17. x = (y +1)2 + 5 8. 4x 2 + 9y 2 = 36 18. x = y 2 9.
x 2 y2 + =1 9 16
19. y 2 − 3x − 2y + 5 = 0
10. (x −1)2 + (y + 3)2 = 20
20. 2y 2 − x 2 + 3y − 4y = 0
11. 9x 2 − y 2 = 9
21. y 2 − x 2 = 25
12. 9x 2 − y 2 + 72x +153 = 0
22. 5y 2 + 4y + 5x 2 − 2x = 25
13. x = (y + 4)2 − 2
23. 3y 2 − 2y + x 2 + 4x − 9 = 0
14. y = (x − 3)2
24. −2y 2 + x − 20y = 49
