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Find the equation for the following circle:

The circle that passes through the origin and has intercepts equal to 1 and 2 on the x- and y-axes, respectively.

  • Math -

    That means it must pass though (0,0), (1,0) and (0,2) . The center must be located where the perpendicular bisectors of chords between those points intersect. That would be the point where the vertical line y = 1 and the horizontal ine x= 1/2 intersect, They cross at (1/2, 1) The radius is the distance of that point from any of the three given point, which is
    R = sqrt[(1/2)^2 + 1^2] = sqrt (5/4)

    Thus the circle equation is
    (x-0.5)^2 + (y-1)^2 = 5/4

    Check my thinking

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