Introduction to Conic Sections

A. Classify the conic.Explain how you know just by looking at the equation.

1. x²+ y²= 36

2. x²- y²= 36

3. 5x²+ 9y²= 45

4. y = 17x²

B.What is the standard equation of thecircle?

5.circle with radius 4, and center (0,0)

6. circle with radius 5, and center (-5, -1)

C. Name the center and radius of the circle.

7. (x-3)²+ y²= 49

D. Statethe vertices of the ellipse.

8. (x²)/25 + (y²)/9 = 1

9. (x²)/9 + (y²)/36 = 1

E. State the center of each conic.

10. ellipse whose equation is (x+1)²/ 4 + (y²)/1 = 1

11. hyperbola whose equation is (x²)/4 - (y²)/9 = 1

12. hyperbola whose equation is [(x+2)²/ 9] - [(y-2)²/ 16] = 1

F. How does the graph of each hyperbola open?Explain how you know.

13. (x²)/9 - (y²)/25 = 1

14. (y²)/4 - (x²)/9 = 1

G. Classify each conic.Explain how you know just by looking at the equation.

15. x²+ 2x + y²+ 6y = 15

16. 9y²- 3 = 18y + 4x

17.y²= x²- 5x + 6