Page 174 - Math Course 3 (Book 2)
P. 174

Circles: Equations





                                                           Your Turn!
                     y
          y = –1
                                                           Equation of a Circle
                                                           Write an equation for a circle with center at (0, –5),
                      5 units    (4, 2)                    d = 18.

                                                           A. x² + (y – 5)² = 81
                     O           5 units                   B. x² + (y + 5)² = 324
                                                     x     C. x² + (y – 5)² = 324
          y = –3                                           D. x² + (y + 5)² = 81
                                                              Answer


                           An equation for the circle is
            Answer
                             (x – 4)² + (y – 2)² = 25.



        Graph a Circle


            Example



         Graph (x – 2)² + (y + 3) ² = 4.
                                                           Use Characteristics of Circles
         Compare each expression in the equation to the    A circle with a diameter of 8 has its center in the
         standard form.                                    second quadrant. The lines y = –1 and x = 1 are
                                                           tangent to the circle. Write an equation of the
            (x – h)² = (x – 2)²     (y – k) ² = (y + 3) ²  circle.
               x – h = x – 2          y – k = y + 3        A. (x – 1)² + (y + 1)² = 16
                 –h = –2                        –k = 3     B. (x – 3)² + (y + 3)² = 16
                                                           C. (x + 3)² + (y – 3)² = 16
                  h = 2                   k = –3           D. (x + 3)² + (y + 3)² = 64
         r² = 4, so r = 2.

         The center is at (2, –3), and the radius is 2.       Answer

         Graph the center. Use a compass set at a width of
         2 grid squares to draw the circle.


                            Answer
                        y







                     O                         X

                          (2, –3)








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