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anonymous

  • one year ago

I don't want anyone to give me the answer, I just need help understanding how to do it please!!

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  1. anonymous
    • one year ago
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    The general form of the equation of a circle is Ax2 + By2 + Cx + Dy + E = 0, where A = B 0. If the circle has a radius of 3 units and the center at (0, 4), which set of values of A, B, C, D, and E correspond to the circle? a)A = 0, B = 0, C = 2, D = 2, and E = 3 b)A = 1, B = 1, C = 8, D = 0, and E = 9 c)A = 1, B = 1, C = 0, D = -8, and E = 7 d)A = 1, B = 1, C = -8, D = 0, and E = 0 e)A = 1, B = 1, C = 8, D = 8, and E = 3

  2. welshfella
    • one year ago
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    if we write the equation of a circle as x^2 + y^2 + 2gx + 2fy + c = 0 then the center is (-g,-f) and the radius is sqrt(g^2 + f^2 - c) note there are no numbers before the x^2 and y^2 in the equation of a circle.

  3. welshfella
    • one year ago
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    so for your circle you can see that A = 1 and B = 1

  4. anonymous
    • one year ago
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    sorry im horrible at math. so do you substitute A and B for X and Y? and D and E for G and F?

  5. welshfella
    • one year ago
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    if we write the 2 equations together we can compare x^2 + y^2 + 2gx + 2fy + c = 0 Ax^2+ By^2 + Cx + Dy + e = 0 can you see that A and B = 1?

  6. welshfella
    • one year ago
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    note x^2 is same as 1x^2

  7. anonymous
    • one year ago
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    ok, so would the answer be B?

  8. welshfella
    • one year ago
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    we dont know that yet we need to find C D and E the center is at (0,4) meaning x = 0 and y = 4 if we compare this with (-g,-f) we see that -g = 0 so C =0 Follow?

  9. welshfella
    • one year ago
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    and in the case of y = 4 , -f = 4 so f = -4 and 2f = -8 making D = 2f = -8

  10. anonymous
    • one year ago
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    ok

  11. welshfella
    • one year ago
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    now to work out e(which = c) we need to solve radius r = sqrt(g^2 + f^2 - c) 3 = sqrt(0^2 + (-4)2 - e)

  12. welshfella
    • one year ago
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    9 = 16 - e

  13. welshfella
    • one year ago
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    so find e and you have your result

  14. anonymous
    • one year ago
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    oh so its C. thank you for showing me how to do it

  15. welshfella
    • one year ago
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    yw

  16. welshfella
    • one year ago
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    yes e = 7 so its C

  17. welshfella
    • one year ago
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    by writing the 2 equations together we can see that C - 2g , D = 2f and E = c

  18. welshfella
    • one year ago
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    - that's called comparing coefficients

  19. anonymous
    • one year ago
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    thank you =D

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