Practice with Graphs of Circles Topic Index | Geometry Index | Regents Exam Prep Center

 Answer the following questions dealing with graphs of circles.
 1. Which of the following equations of a circle has center at (1,-3) and radius of 5? Choose: Explanation Be careful.  The center coordinates are always subtracted from x and y.  When you subtract a negative 3 it becomes +3.

 2. What is the equation of a circle whose diameter is 24 and whose center is at the origin? Choose: Explanation Remember to cut the diameter in half to get the radius.  The radius is 12.

 3. An ambulance company provides services within an 80 mile radius of their headquarters.  If this service area is represented graphically,  with the headquarters located at the coordinates (0,0), what is the equation that represents the service area? Choose: Explanation The radius in this problem is 80.  You need to square 80 and place it into the formula.

 4. What are the coordinates of the center of this circle? Choose: (3,5) (-3,5) (-3,-5) (3,-5) Explanation Be careful when reading the x coordinate. The (x+3) gives an x coordinate of -3.

 5. What are the coordinates of the center of this circle? Choose: (7,7) (0,7) (-7,-7) (0,-7) Explanation The first coordinate is 0.  Remember x-0=x. The second coordinate is -7.  Consider (x-(-7)).

 6. The point (1,2) is on the circle whose equation is Choose: True False Explanation Substitute x=1 and y=2 into the equation and see if the answer is true.  It is true.

 7. The center of a circle represented by the equation is located in Quadrant _____. Choose: I II III IV Explanation The center is (2-3). This point is in Quadrant 4.

 8. What are the coordinates of the center of the circle represented by the equation  ? Choose: (3,4) (3,-4) (-3,4) (-3,-4) Explanation Remember that (x+3) is really (x-(-3)). The center is (-3,4).

 9. What is the equation of a circle with center (-3,1) and radius 7? Choose: Explanation Remember that (x-(-3)) becomes (x+3).

 10. A circle has the equation  . What are the coordinates of its center and the length of its radius? Choose: (-1,3) and 4 (1,-3) and 4 (-1,3) and 16  (1,-3) and 16 Explanation Remember that (x+1) is really (x-(-1)). Center (-1, 3) radius 4

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