Equation of a circle

1. Dec 11, 2008

nobahar

1. The problem statement, all variables and given/known data
This is from one of the online textbooks recommended on the site, but it only has selected answers and this one's not included.
A circle passes through the points (0,0), (0,1) and (2,0). What is it's equation.

2. Relevant equations
I think the form is the (y1-y0)2+(x1-x0)2=r2.
So I got (y-1/2)2+(x-1)2=r2. Since the radius has to extend to each of these points from the centre, I think this does it. Apologies for the hurried post, I will elaborate as soon as possible if necessary, but I think this is enough information (my computrers broke so I have to use a library one!... and there's only five minutes left!).
Is this answer right? Or have I misunderstood?!

2. Dec 11, 2008

HallsofIvy

Staff Emeritus
Okay, so you say you have calculated the center of the circle to be (1, 1/2)? How did you get that? (I can think of three ways. I suspect you used the simplest.) Assuming that is correct, all you need to do is determine r: Find the distance from (1, 1/2) to any one of those points (or try all three as a check).

3. Dec 12, 2008

nobahar

Sorry, I thought about it last night after I posted and realised I could put in r. I got $$\frac{\sqrt{5}}{2}$$. I tried it and it works. I think...?
You mentioned three ways of finding the equation, could you elaborate as I would greatly appreciate it. I based it on that two of the points share the y-axis and two of the points share the x-axis, and deduced that the radius has to extend to all these points. (thanks for pointing out that I probably used the simplest method, very encouraging...)
As always, thankyou for the response, and thanks in advance.