SOLUTION: a circle passes through the point (9,3) and has a center (2,27). write the equation. give me a step by step on how to do it

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: a circle passes through the point (9,3) and has a center (2,27). write the equation. give me a step by step on how to do it      Log On


   

Question 198100: a circle passes through the point (9,3) and has a center (2,27). write the equation. give me a step by step on how to do it
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The general equation for a circle in xy-plane is:
%28x+-+x%5B0%5D%29%5E2+%2B+%28y+-+y%5B0%5D%29%5E2+=+r%5E2
x%5B0%5D and y%5B0%5D are coordinates of the center,
given as (2,27)
r is the radius.
I can plug in (2,27)
%28x+-+2%29%5E2+%2B+%28y+-+27%29%5E2+=+r%5E2
x and y in the equation are ANY x and
y on the circle, so if I plug in (9,3) , that is a
valid solution, and I can then solve for r
%289+-+2%29%5E2+%2B+%283+-+27%29%5E2+=+r%5E2
7%5E2+%2B+%28-24%29%5E2+=+r%5E2
49+%2B+576+=+r%5E2
r%5E2+=+625
r+=+25
The equation is:
%28x+-+2%29%5E2+%2B+%28y+-+27%29%5E2+=+625