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10.07Circles in the Coordinate Plane

In problems 1-3, determine the center and radius of the circle with the equation given.

  1. (x – 3)2 + (y – 3)2 = 25

Center: (,)

Radius =

  1. (x – 1)2 + (y + 2)2 = 9

Center: (, )

Radius =

  1. (x + 3)2 + (y + 4)2 = 1

Center: (,

Radius:

For problems 4-7, write the equation for circle O based on the given information.

  1. center (3, -2), radius 4

equation: ()2 + ()2 =

  1. center (0, 5), radius

equation: ()2 + ()2 =

  1. center (2, -4), point (2, 1) lies on the circle

equation: ()2 + ()2 =

  1. points (1, 5) and (1, 11) lie on a diameter of the circle.

equation: ()2 + ()2 =

  1. Graph the equation (x – 1)2 + (y + 3)2 = 9. Drag the center to the appropriate location and label it. Then, drag and adjust the circle. (Hint – use the one of the corners to re-size the circle without changing its shape.) Place the radius (adjusting its length) as well.

  1. Graph the equation x2 + y2 = 25. Drag the center to the appropriate location and label it. Then, drag and adjust the circle. (Hint – use the one of the corners to re-size the circle without changing its shape.) Place the radius (adjusting its length) as well.
  1. A town sits at point (5, 1) on a map. From the tallest building in the town, you can see objects up to 7 miles away. If each unit on the map is equivalent to 1 mile, can you see a statue in a town at point (2, 5)? Explain.
  1. Hurricane Andrew landed at Lafayette, LA in 1992. When Lafayette was in the eye of the hurricane, its outer boundary stretched to Vicksburg, Mississippi. If Lafayette, LA is 260 miles from Vicksburg, MS, write an equation for the circle occupied by the hurricane. Assign Lafayette the coordinates (0, 0).