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anonymous

  • one year ago

Does anyone know how to do this? Circle O, with center (x, y), passes through the points A(0, 0), B(–3, 0), and C(1, 2). Find the coordinates of the center of the circle.

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  1. campbell_st
    • one year ago
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    use the distance formula as the distance from any point on the circumference is always equal so OA = Ob = OC this will give the equation or locus or the circle you'll then need to factor it to a standard form

  2. triciaal
    • one year ago
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    |dw:1436990750032:dw|

  3. triciaal
    • one year ago
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    center (0,0) |dw:1436990958298:dw|

  4. triciaal
    • one year ago
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    equation of a circle with center (0,0) x^2 + y^2 = r^2 where r is the radius in this sketch the radius is OR

  5. triciaal
    • one year ago
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    |dw:1436991295757:dw|

  6. triciaal
    • one year ago
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    one approach is to plot the points first then as above also given by @campbell_st find OA, OB and OC same as OR in the sketch solve for (x,y)

  7. triciaal
    • one year ago
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    do you see how to do it now?

  8. anonymous
    • one year ago
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    I hate to ask but Do you guys know the answer, I mean I would do it but I just wanna finish this homeschool already

  9. triciaal
    • one year ago
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    I would have to do the problem

  10. campbell_st
    • one year ago
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    if you use the distance formula OA = OB then \[\sqrt{(x - 0)^2 + (y - 0)^2} = \sqrt{(x + 3)^2 + (y - 0)^2}\] so this becomes \[x^2 + y^2 = x^2 + 6x + 9 + y^2\] this will allow you to solve for x. to get y use the distance between OA and OC \[\sqrt{(x - 0)^2 + (y - 0)^x} = \sqrt{(x -1)^2+(y - 2)^2}\] which becomes \[x^2 + y^2 = (x -1)^2 + (y -2)^2\] substitute the answer for x that you got in the previous calculation then solve for y

  11. campbell_st
    • one year ago
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    well I have an answer, and the centre contains fractional values for x and y

  12. triciaal
    • one year ago
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    post your answer and will check it later

  13. anonymous
    • one year ago
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    |dw:1437175931767:dw|

  14. triciaal
    • one year ago
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    |dw:1436992391537:dw|

  15. anonymous
    • one year ago
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    I found an answer for x which is -1.5 but the answer I got for y is 1/4(5-2x)

  16. anonymous
    • one year ago
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    Is that correct

  17. triciaal
    • one year ago
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    |dw:1436992999048:dw|

  18. triciaal
    • one year ago
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    sorry have to leave

  19. anonymous
    • one year ago
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    Its okay Ill figure out the y part

  20. triciaal
    • one year ago
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    |dw:1437015241447:dw|

  21. triciaal
    • one year ago
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    center (x, y) = (-3/2, 1/2)

  22. triciaal
    • one year ago
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    yes what you have for y is incomplete substitute the value for x

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