1. Equations of Ellipses & Hyperbolas If the equation is in standard form we need to change it into the usable form …

2. Equations of Ellipses & Hyperbolas If the equation is in standard form we need to change it into the usable form … EXAMPLE :Find the center, major / minor vertices, and foci and for :

3. Equations of Ellipses & Hyperbolas If the equation is in standard form we need to change it into the usable form … EXAMPLE :Find the center, major / minor vertices, and foci and for : Get your x’s and y’s together, move any constant to the other side…

4. Equations of Ellipses & Hyperbolas If the equation is in standard form we need to change it into the usable form … EXAMPLE :Find the center, major / minor vertices, and foci and for : Divide the x’s and y’s by the coefficient of the quadratic term…

5. Equations of Ellipses & Hyperbolas If the equation is in standard form we need to change it into the usable form … EXAMPLE :Find the center, major / minor vertices, and foci and for : We are now ready to complete the square…

6. Equations of Ellipses & Hyperbolas If the equation is in standard form we need to change it into the usable form … EXAMPLE :Find the center, major / minor vertices, and foci and for : Be sure to multiply the outside coefficient by the squared answer and fill in the blanks on right side…

7. Equations of Ellipses & Hyperbolas If the equation is in standard form we need to change it into the usable form … EXAMPLE :Find the center, major / minor vertices, and foci and for : Be sure to multiply the outside coefficient by the squared answer and fill in the blanks on right side…

8. Equations of Ellipses & Hyperbolas If the equation is in standard form we need to change it into the usable form … EXAMPLE :Find the center, major / minor vertices, and foci and for : Be sure to multiply the outside coefficient by the squared answer and fill in the blanks on right side…

9. Equations of Ellipses & Hyperbolas If the equation is in standard form we need to change it into the usable form … EXAMPLE :Find the center, major / minor vertices, and foci and for : Combine the constants and fill in blank…

10. Equations of Ellipses & Hyperbolas If the equation is in standard form we need to change it into the usable form … EXAMPLE :Find the center, major / minor vertices, and foci and for : Divide everything by the constant on the right…

11. Equations of Ellipses & Hyperbolas If the equation is in standard form we need to change it into the usable form … EXAMPLE :Find the center, major / minor vertices, and foci and for : Here is the new equation where we can see ( h, k ), a, b, etc…

12. Equations of Ellipses & Hyperbolas If the equation is in standard form we need to change it into the usable form … EXAMPLE :Find the center, major / minor vertices, and foci and for : a = 4 b = 1 c =

13. Equations of Ellipses & Hyperbolas If the equation is in standard form we need to change it into the usable form … EXAMPLE :Find the center, major / minor vertices, and foci and for : a = 4 b = 1 c = Center ( 2, - 1 ) ( x ) Major vertices ( 6, - 1 ), ( - 2, - 1 ) ( y ) Minor Vertices ( 2, 0 ), ( 2, -2 ) ( x ) Foci ( 2 ±, - 1 ) ±4±1

14. Equations of Ellipses & Hyperbolas EXAMPLE # 2 :Find the center, major vertices, foci, and asymptote equation for :

15. Equations of Ellipses & Hyperbolas EXAMPLE # 2 :Find the center, major vertices, foci, and asymptote equation for : Got x’s and y’s together, placed constant on other side…

16. Equations of Ellipses & Hyperbolas EXAMPLE # 2 :Find the center, major vertices, foci, and asymptote equation for : Divided by the squares’ coefficients…

17. Equations of Ellipses & Hyperbolas EXAMPLE # 2 :Find the center, major vertices, foci, and asymptote equation for : Set up completing the square…

18. Equations of Ellipses & Hyperbolas EXAMPLE # 2 :Find the center, major vertices, foci, and asymptote equation for : Complete the square…

19. Equations of Ellipses & Hyperbolas EXAMPLE # 2 :Find the center, major vertices, foci, and asymptote equation for : Completed the square…

20. Equations of Ellipses & Hyperbolas EXAMPLE # 2 :Find the center, major vertices, foci, and asymptote equation for : Divide everything by right side…

21. Equations of Ellipses & Hyperbolas EXAMPLE # 2 :Find the center, major vertices, foci, and asymptote equation for : New equation…

22. Equations of Ellipses & Hyperbolas EXAMPLE # 2 :Find the center, major vertices, foci, and asymptote equation for : I rewrote the equation to show the positive part leading…

23. Equations of Ellipses & Hyperbolas EXAMPLE # 2 :Find the center, major vertices, foci, and asymptote equation for : a = 4 b = 2 c =

24. Equations of Ellipses & Hyperbolas EXAMPLE # 2 :Find the center, major vertices, foci, and asymptote equation for : a = 4 b = 2 c = Center( - 8, 2 )Notice the order !!! Major Vertices( -8, 4 ), ( -8, 0 )Change y by ± 2 Foci( -8, 2 ± )Change y by ± Asymptote equation :