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Writing equations of conics in vertex form

Writing equations of conics in vertex form. MM3G2. 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

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Writing equations of conics in vertex form

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  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: • Example 1 • Step 1: move the constant to the other side of the equation and move common variables together

  4. Example 1 • Step 2: Group the x terms together and the y terms together • Step 3: Factor the GCF (coefficient)from the x group and then from the y group

  5. Example 1 • Step 4: Complete the square on the x group (don’t forget to multiply by the GCF before you add to the right side.) Then do the same for the y terms 6/2 = 3 2/2 = 1 12 = 1 32 = 9

  6. Example 1 • Step 5: Write the factored form for the groups. Now we have to make the equation equal 1 and that will give us our denominators

  7. Example 1 • Step 6: Divide by the constant.

  8. Example 1 • Step 7: simplify each fraction. Now the equation looks like what we are used to 1 4 9

  9. Example 2: Ellipse

  10. Example 2 -6/2 = -3 -8/2 = -4 -42 = 16 -32 = 9

  11. Example 2 1 4 25

  12. Example 3: Ellipse

  13. Example 3 -10/2 = -5 4/2 = 2 22 = 4 -52 = 25

  14. Example 3 1 81 36

  15. Example 4: Hyperbola

  16. Example 4 6/2 = 3 2/2 = 1 12 = 1 32 = 9

  17. Example 4 1 2

  18. Example 5: Hyperbola

  19. Example 5 -8/2 = -4 4/2 = 2 22 = 4 -42=16

  20. Example 5 1 9 4

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