MATH

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two circles whose equations are (x-3)^2+(y-5)^2=25 and (x-7)^2+(y-5)^2=9 intersect in two points. What is the equation of the line passing through these two points?


Can anyone please give me some ideas how to do it without graphing it out? THANKS A LOT!

  • MATH -

    The centers are at (3,5) and at (7,5) along the horizontal line y = 5 and 7-3 = 4 apart
    left radius = 5
    right radius = 3
    so
    the points lie on vertical line x = something an equal distance above and below y = 5
    so
    triangle
    base = 4 along y = 5 line
    left leg = 5
    right leg = 3
    let's use law of cosines to find the angle on the left, between the y = 5 line and the long side length 5
    3^2 = 5^2 + 4^2 - 2*5*4 cos A
    9 = 25 + 16 - 40 cos A
    32 = 40 cos A
    A = 36.87 degrees
    now the distance from x = 3 to our desired vertical line is
    5 cos A which is 5 (32/40) = 4
    so our line is
    x = 3 + 4 = 7
    which we could have said earlier seeing that our triangle is
    3, 4, 5 and therefore a right triangle

  • MATH -

    What do you mean?

  • MATH -

    What do youm mean?

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