SOLUTION: What is the standard equation for the circle that passes through the points: (-5, 0) (0, 4) (2, 4)

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: What is the standard equation for the circle that passes through the points: (-5, 0) (0, 4) (2, 4)      Log On


   

Question 875794: What is the standard equation for the circle that passes through the points:
(-5, 0)
(0, 4)
(2, 4)
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
What is the standard equation for the circle that passes through the points:
(-5, 0)
(0, 4)
(2, 4)
**
Standard form of equation for a circle: %28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2,(h,k)=center, r=radius
3 equations:
%28-5-h%29%5E2%2B%280-k%29%5E2=r%5E2
%280-h%29%5E2%2B%284-k%29%5E2=r%5E2
%282-h%29%5E2%2B%284-k%29%5E2=r%5E2
..
25+10h+h^2+k^2=r^2
h^2+16-8k+k^2=r^2
(4-4h+h^2+16-8k+k^2=r^2
..
9+10h+8k=0
5+14h+8k=0
-4+4h=0
h=1
8k=-19
k=-19/8
r^2=6^2+(-19/8)^2≈41.64
equation for the circle: %28x-1%29%5E2%2B%28y%2B%2819%2F8%29%29%5E2=41.64 (approximate only, due to rounding errors)