Is My Equation for a Circle Through Points (0,0), (0,1), and (2,0) Correct?

[nobahar]

Homework Statement

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.

Homework 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?!
Thanks in advance.

 

[HallsofIvy]

Homework Statement

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.

Homework 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?!
Thanks in advance.

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 anyone of those points (or try all three as a check).

 

[nobahar]

Sorry, I thought about it last night after I posted and realized 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.