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Graphing Circles - Finding the radius

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A circle is tangent to the y-axis at the point (0,2) and passes through the point (8,0). Find the radius of the circle.

I tried using distance formula but it doesnt work? Help please thanks.

  • Graphing Circles - Finding the radius -

    since the line y = 2 is tangent to the circle, its centre must lie on the y-axis

    let the centre be (0,b)

    the equation of the circle is
    x^2+ (y-b)^2 = r^2

    but (0,2) lies on it ----> (2-b)^2 = r^2

    but (8,0) lies on it ----> 64 + (0-b)^2 = r^2
    64 +b^2= r^2

    then 64 + b^2 = (2-b)^2
    64 + b^2 = 4-2b+b^2

    60 = -2b
    b = -30

    the centre is (0, -30) ---> radius = 2-(-30) = 32

    OR

    distance from (0,b) to (0,2) must equal the distance from (0,2) to (8,0)

    2-b = √(64 + b^2)
    square both sides
    4-2b+b^2 = 64+b^2
    -2b = 60
    b = -30
    the radius is 2 - (-30) = 32

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