1 / 24

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

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

hieu
Télécharger la présentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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 = ±4 ±1 Center ( 2 , - 1 ) ( x ) Major vertices ( 6 , - 1 ) , ( - 2 , - 1 ) ( y ) Minor Vertices ( 2 , 0 ) , ( 2 , -2 ) ( x ) Foci ( 2 ± , - 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 :

More Related