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Writing equations of conics in vertex form

Writing equations of conics in vertex form. MM3G2. Write the equation for the circle in vertex form :. Example 1 Step 1: Move the constant to the other side of the equation & put your common variables together. Example 1.

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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. Write the equation for the circle in vertex form: • Example 1 Step 1: Move the constant to the other side of the equation & put your common variables together

  3. Example 1 • Step 2: Identify the coefficients of the squared terms and divide everything by that coefficient. • Both coefficients are 1 so divide everything by 1

  4. Example 1 • Step 3: Group the x terms together and the y terms together using parenthesis.

  5. Example 1 • Step 4: Complete the square for the x terms Then for the y terms

  6. Example 1 • Step 5: Write the factored form for the groups. What is the center of this circle? What is the radius?

  7. Write the equation for the circle in vertex form: • Example 2 • Step 1: Move the constant to the other side of the equation & put your common variables together

  8. Example 2 • Step 2: Identify the coefficients of the squared terms and divide everything by that coefficient. • Both coefficients are 2 so divide everything by 2

  9. Example 2 • Step 3: Group the x terms together and the y terms together using parenthesis.

  10. Example 2 • Step 4: Complete the square for the x terms Then for the y terms

  11. Example 2 • Step 5: Write the factored form for the groups. What is the center of this circle? What is the radius?

  12. Write the equation for the circle in vertex form: • Example 3 • Step 1: Move the constant to the other side of the equation & put your common variables together

  13. Example 3 • Step 2: Identify the coefficients of the squared terms and divide everything by that coefficient. • Both coefficients are 4 so divide everything by 4

  14. Example 3 • Step 3: Group the x terms together and the y terms together using parenthesis.

  15. Example 3 • Step 4: Complete the square for the x terms Then for the y terms

  16. Example 3 Step 5: Write the factored form for the groups. What is the center of this circle? What is the radius?

  17. Write the equation for the circle in vertex form: • Example 4 • Step 1: Move the constant to the other side of the equation & put your common variables together

  18. Example 4 • Step 2: Identify the coefficients of the squared terms and divide everything by that coefficient. • Both coefficients are 5 so divide everything by 5

  19. Example 4 • Step 3: Group the x terms together and the y terms together using parenthesis.

  20. Example 4 • Step 4: Complete the square for the x terms Then for the y terms

  21. Example 4 • Step 5: Write the factored form for the groups. What is the center of this circle? What is the radius?

  22. 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:

  23. Write the equation for the ellipse in vertex form: • Example 5 • Step 1: Move the constant to the other side of the equation and move common variables together

  24. Example 5 • 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

  25. Example 5 • 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

  26. Example 5 • 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

  27. Example 5 • Step 6: Divide by the constant.

  28. Example 5 • Step 7: simplify each fraction. Now the equation looks like what we are used to!! 1 4 9

  29. What is the center of this ellipse? • What is the length of the major axis? • What is the length of the minor axis?

  30. Example 6: Ellipse Step 1: Step 2: Step 3:

  31. Example 6 Step 4: Step 5:

  32. Example 6 Step 6: 1 4 25

  33. What is the center of this ellipse? • What is the length of the major axis? • What is the length of the minor axis?

  34. Example 7: Ellipse Step 1: Step 2: Step 3:

  35. Example 7 Step 4: Step 5:

  36. Example 7 Step 6: 1 81 36

  37. What is the center of this ellipse? • What is the length of the major axis? • What is the length of the minor axis?

  38. Example 8: Hyperbola Step 1: Step 2: Step 3:

  39. Example 8 Step 4: Step 6:

  40. Example 8 Step 6: 1 2

  41. What is the center of this hyperbola? • What is the length of the transverse axis? • What is the length of the conjugate axis?

  42. Example 9: Hyperbola Step 1: Step 2: Step 3:

  43. Example 9 Step 4: Step 5:

  44. Example 9 Step 6: 1 9 4

  45. What is the center of this hyperbola? • What is the length of the transverse axis? • What is the length of the conjugate axis?

  46. You Try! • Write the equation of each conic section in vertex form: Identify the center of each conic section as well as the length of the major/minor or transverse/conjugate axis.

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