MODERATE EXERCISES

(4) Find the equation of each circle described below:

 (a) center at the origin and passing through (4,7)

 (b) center at (3,-2) and has y-intercept at -1.

 (c) endpoints of a diameter are (-2,3) and (3,-1).
 
 (d) center at (3,5) and tangent to the x-axis.

 (a) radius2 = (7 - 0)2 + (4 - 0)2
             = 49 + 16 = 65

     (x - 0)2 + (y - 0)2 = radius2
     x2 + y2 = 65


 (b) (x - 3)2 + (y + 2)2 = A
     (0 - 3)2 + (-1 + 2)2 = A
     9 + 1 = A
     A = 10

     (x - 3)2 + (y + 2)2 = 10


 (c) diameter2 = (3 - (-2))2 + (-1 - 3)2
               = 52 + 42
               = 25 + 16 = 41

     radius2 = diameter2/4 = 41/4

     using the midpoint formula to find the center of the circle we get:
     x = (3 - 2)/2 = 1/2
     y = (-1 + 3)/2 = 2/2 = 1

     (x - 1/2)2 + (y - 1)2 = 41/4


 (d) (x - 3)2 + (y - 5)2 = 25