1. WRITING EQUATIONS OF CONICS IN VERTEX FORM MM3G2

2. Recall:  The equation for a circle does not have denominators  The equation for an ellipse and a hyperbola do have denominators  The equation for a circle is not equal to one  The equation for an ellipse and a hyperbola are equal to one  We have a different set of steps for converting ellipses and hyperbolas to the vertex form:

3. Write the equation for the ellipse in vertex form:

4. Example 1

5. 2/2 = 1 1 2 = 1 6/2 = 3 3 2 = 9

6. Example 1

8. 9 4 1

9. Example 2: Ellipse

10. Example 2 -8/2 = -4 -4 2 = 16 -6/2 = -3 -3 2 = 9

11. Example 2 25 4 1

12. Example 3: Ellipse

13. Example 3 4/2 = 2 2 2 = 4 -10/2 = -5 -5 2 = 25

14. Example 3 36 81 1

15. Example 4: Hyperbola

16. Example 4 2/2 = 1 1 2 = 1 6/2 = 3 3 2 = 9

17. Example 4 2 1

18. Example 5: Hyperbola

19. Example 5 4/2 = 2 2 2 = 4 -8/2 = -4 -4 2 =16

20. Example 5 9 4 1