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    Write the equation of a circle centered at (3,4) with a radi

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    Write the equation of
    a. a circle centered at (3,4) with a radius 5

    (See attached file for full problem description)

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    a. The equation for a circle is
    (x - h)2 + (y - k)2 = r2
    where h and k are the x- and y-coordinates of the center of the circle and r is the radius. So in this problem the equation for the circle centered at (3,4) and r = 5 is:
    (x - 3)2 + (y - 4)2 = 25

    b. Let y = ax + b. This line goes thru (-1,3) and (5,18) hence:
    -a + b = 3 OR b = a +3
    5a + b = 18
    Substitute b = a + 3 into the above:
    5a + a + 3 = 18
    Hence 6a = 15 or a =15/6 =2.5
    And therefore b = 5.5
    The line has the form y = 2.5x + 5.5

    c. Choose some point having coordinates (x,y). The distance between this point and (-5,4) is given by:

    The distance between point (x,y) and (3,16) is given by

    Equating these distances, since the point is to be equidistant from the two given points, we have:
    Squaring both sides, we have:


    Substitute one into the other:

    Hence the points of intersection are (0.5,0.87) and (-0.5,-0.87)


    Solution Summary

    The solution provides detailed and step-by-step instructions, including drawings, in 10 pages of Word and Excel on how to solve these algebra problems.