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deerhunter15

  • one year ago

The equation below represents a circle. x​2​ + ​y​2​ + 4​x​ – 2​y​ = ​a Part A: What is the ​x​ coordinate of the center of the circle? Part B: What is the ​y​ coordinate of the center of the circle? Part C: What is the value of ​a​ in the equation if the radius of the circle is 8?

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  1. welshfella
    • one year ago
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    do you know how to complete the square?

  2. deerhunter15
    • one year ago
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    no @welshfella I've never learned this stuff :/

  3. deerhunter15
    • one year ago
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    @welshfella

  4. welshfella
    • one year ago
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    x^2 + 4x = (x + 2)^2 - 4 you divide the coefficient of x by 2 - in this case its 4/2 = 2 so this gives(x + 2) ^2 when you expand that you get +4 so you have to subtract 4 so that its = to x^2 + 4x.

  5. welshfella
    • one year ago
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    we intend to convert the equation of the circle to the standard form (x - a)^2 + (y - b)^2 = r^2 here (a,b) is the center of circle and r = radius

  6. welshfella
    • one year ago
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    so comparing (x - a) and ( x + 2) we see that -a = + 2 give a = -2 so -2 is the x coordinate of the center of circle

  7. welshfella
    • one year ago
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    now you can work out the y coordinate in a sismilar way by completing the square on y^2 - 2y

  8. welshfella
    • one year ago
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    try doing that

  9. deerhunter15
    • one year ago
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    ok I will try

  10. welshfella
    • one year ago
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    I'll start you off;- y^2 - 2y divide -2 by 2 = -1 so we have (x - 1)^2 - A what will A be?

  11. deerhunter15
    • one year ago
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    -1x^2=A @welshfella

  12. welshfella
    • one year ago
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    no A willo be -1 because (x - 1)^2 = x^2 - 2x + 1 so to get this back to x^2 - 2x we have to subtract 1

  13. deerhunter15
    • one year ago
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    oh

  14. deerhunter15
    • one year ago
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    @welshfella whats y?

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