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Math Help - Circle Graphs

  1. #1
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    Circle Graphs

    For each question below, there is a circle given in the textbook with information. I will explain with words what each graph displays in the book.

    Instructions for BOTH circles:

    (a) Find the center and radius of each circle.

    (b) Write the standard form of the equation of each circle?

    CIRCLE A PICTURE HAS:

    Point (1, 0) on the circle and point (1, 2) in what appears to be the center of the circle.

    CIRCLE B PICTURE HAS:

    Point (0, 1) on the circle and point (2, 3) also on the circle.
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  2. #2
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    Hello, symmetry!

    You're expected to know the general equation of a circle.

    Given: center (h,k) and radius r
    . . . . . the equation is: . (x-h)^2 + (h - k)^2\:=\:r^2


    Find the center and radius of each circle.
    Write the standard form of the equation of each circle.

    [1] CIRCLE A PICTURE HAS:
    Point (1, 0) on the circle and point (1, 2) in what appears to be the center of the circle.

    You already know the center: . (h,k) = (1,2)

    The radius is the distance from the center (1,2) to the point (1,0).
    . . You can see that the distance is 2, right?

    Write the equation: . (x-1)^2 + (y-2)^2\:=\:2^2



    [2] CIRCLE B PICTURE HAS:
    Point (0, 1) on the circle and point (2, 3) also on the circle.

    There is not enough information to determine a specific circle.

    My guess is that these two points are the ends of a diameter.

    If that's true, the center is the midpoint M between the two points.
    . . Use the Midpoint Formula to find it.

    Then use the Distance Formula to find the distance from M to one of the points.
    . . That, of course, is the radius.

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  3. #3
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    ok

    This is exactly what I was looking for in terms of an answer.

    Yes, each point on the graph lies on the circle at the end of a diameter.
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