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Consider the circle that is centered at the origin and contains the point .

  1. Use geometry and the definition of a circle to prove or disprove that the point  lies on this circle.

    Any line from the origin to the edge of the circle will be units long.

    Find the distance from the origin to .

  2. Calculate at least one value of such that the point  lies on the circle.


  3. Name three other points on the same circle.

    Write the equation for this circle and find values of and that satisfy the equation.