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

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 = 100^1/2

 

     r= 10

 

The final equation is:

 

     (x-5)² + (y+4)² = 10²