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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 …

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

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  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 :

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