Question

A circle is centered at the point (5,-4) And passes through the point (-3,2). What is the equation of the circle?

Answer 1

The equation of a circle is:

(x-h)2 + (y-k)2 = r2

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 = r2
(x-5)2 + (y+4)2 = r2

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 = [82 + (-6)2]1/2
r = [64 + 36]1/2
r = 1001/2

r= 10

The final equation is:

(x-5)2 + (y+4)2 = 102