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anonymous

  • 5 years ago

The center of the circle that passes through the points (-2,3), (0,-3), and (4,-3) is________ a) (2,2) b) there is not enough data to find the center c) (1,2) d) (2,1)

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  1. anonymous
    • 5 years ago
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    first we can find the eq of circle passing through three points, then can check the centre

  2. anonymous
    • 5 years ago
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    how do I do that?

  3. anonymous
    • 5 years ago
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    general eq of the circle is \[x^2+y^2+2gx+2fy+c=0\]

  4. anonymous
    • 5 years ago
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    substitute the three points in this eq we get three eqs in three unknows find the unknows g,f and c

  5. anonymous
    • 5 years ago
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    centre is \[\sqrt{g^2+f^2-c}\]

  6. anonymous
    • 5 years ago
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    for(-2,3) 4+9-4g+6f+c=0

  7. anonymous
    • 5 years ago
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    for(0,-3) 9-6f+c=0

  8. anonymous
    • 5 years ago
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    for(4,-3) 16+9+8g-6f+c=0

  9. anonymous
    • 5 years ago
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    -4g+6f+c=-13 -6f+c=-9 8g-6f+c=-25

  10. anonymous
    • 5 years ago
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    subtracting 1 n 3 -12g+12f=12 -g+f=1

  11. anonymous
    • 5 years ago
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    sub 1 n 2 -4g+12f=-4 g-3f=1

  12. anonymous
    • 5 years ago
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    adding the resultant eqs -2f=2 f=-1 which gives g=-2 n c=-3

  13. anonymous
    • 5 years ago
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    center=(-g,-f)=(2,1)

  14. anonymous
    • 5 years ago
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    so D is the right option:)

  15. anonymous
    • 5 years ago
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    m sorry the formula i wrote earlier is to find the radius

  16. anonymous
    • 5 years ago
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    thank you for your help

  17. anonymous
    • 5 years ago
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    u got all the lenghy computations?

  18. anonymous
    • 5 years ago
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    lengthy*

  19. anonymous
    • 5 years ago
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    for the most part

  20. anonymous
    • 5 years ago
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    what do g and f represent though?

  21. anonymous
    • 5 years ago
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    if there is some confusion, u can ask:)

  22. anonymous
    • 5 years ago
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    these r constants

  23. anonymous
    • 5 years ago
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    the eq i wrote is the general eq of the circle

  24. anonymous
    • 5 years ago
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    finding out g,f and c, we can find the eq of the circle

  25. anonymous
    • 5 years ago
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    okay thank you

  26. anonymous
    • 5 years ago
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    welcome:)

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