Advanced Math

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write the equation of the circle that satisfies each set of conditions.

the center of the circle is on the x-axis, its radius is 1, and it passes through the point (square root of 2 over 2, square root of two over 2)

  • Advanced Math -

    Circle equation generally:
    (x-a)^2 + (y-b)^2 = r^2

    The center is in x-axis (b = 0), giving:
    (x-a)^2 + y^2 = 1
    ((sqrt(2)/2)-a)^2 + (sqrt(2)/2)^2 = 1
    ((sqrt(2)/2)-a)^2 + (1/2) = 1
    (sqrt(2)/2)-a = ±sqrt(1/2)

    (sqrt(2)/2)-a = sqrt(1/2)
    a = 0
    So: x^2 + y^2 = 1

    (sqrt(2)/2)-a = -sqrt(1/2)
    a = sqrt(2)
    So: (x-sqrt(2))^2 + y^2 = 1

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