Question

A circle is centered at the point (5,-4) and passes through (-3,2). The equation of this circle is (x+___)²+(y+___)²=____.

Answer 1

The equation of a circle is:
 (x-h)^2 + (y-k)^2 = r^2
 where (h,k) is the location of the center and r is the radius.  So we need to find h, k, and r.  The center is given as (5,-4) so h = 5 and k = -4:
 (x-5)^2 + (y-(-4))^2 = r^2
 (x-5)^2 + (y+4)^2 = r^2
 So we need to find r.  Use the distance formula to find the distance between (5,-4) and (-3,2):
 r = [(5-(-3))^2+((-4)-2)^2]^1/2
 r = [8^2 + (-6)^2]^1/2
 r = [64 + 36]^1/2
 r = 100^1/2
 r= 10
 The final equation is:
 (x-5)^2 + (y+4)^2 = 10^2