Now you have looked at equations of circles in both standard and in graphing form and have graphed circles and identified equations from the graphs.

Further explore the attributes of the equation of a circle by interacting with the applet linked below.

After exploring the circle applet, return to this resource and answer the questions below using your notes.

This activity might not be viewable on your mobile device.interactive exercise, assistance may be required Circle Geogebra Applet


  1. What does the variable "r" represent?
    Interactive popup. Assistance may be required.

    Check Your Answer

    "r" represents the radius of the circle (the distance from the center to any point on the circle).Close Pop Up

  2. As "r" changes what happens to the graph?
    Interactive popup. Assistance may be required.

    Check Your Answer

    As "r" gets larger, the circle grows larger and as "r" gets smaller, the circle grows smaller—the radius changes with changes in "r".Close Pop Up

  3. How is segment AC (on the graph of the applet) related to "r"?
    Interactive popup. Assistance may be required.

    Check Your Answer

    The segment AC is a radius of the circle, therefore it is “r” units long.Close Pop Up

  4. How does your graph change as you change "h" and as you change "k" (be specific)?
    Interactive popup. Assistance may be required.

    Check Your Answer

    A change in “h” is a change in the abscissa (x-value) of the center point of the circle. This change results in a horizontal movement of the circle on the plane. A change in “k” is a change in the ordinate (y-value) of the center point of the circle. This change results in a vertical movement of the circle on the plane.Close Pop Up

  5. Where is the center of the circle when the equation is (x − 3)2 + (y − -2)2 = 1?
    Interactive popup. Assistance may be required.

    Check Your Answer

    The center is (3, -2) as h = 3 and k = -2.Close Pop Up

  6. What is the radius of this circle?
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    Check Your Answer

    radius = √1 = 1 Close Pop Up

  7. As you move point A around the circle does the segment AC stay the same length?
    Interactive popup. Assistance may be required.

    Check Your Answer

    The length of the segment AC remains the same (the radius of the circle) as A (a point on the circle) moves anywhere on the circle.Close Pop Up

  8. Verify this with the distance formula for several points that are not on the x-axis or the y-axis. Go to the applet and move point A around the circle, choosing several different points and use the distance formula or Pythagorean Theorem to prove the distance (length of hypotenuse) does not change.
    Interactive popup. Assistance may be required.

    Check Your Answer

    Example: Point A: (-1.73,1)
    Distance to center (0, 0):

    Point A: (0, 2) Distance to center (0, 0) Close Pop Up