Equation of a circle, given three intercepts

[Guest]

i'll not familiar with this type of problem so i wasn't sure how to start it. i could really use some help.
a circle passes through the origin and has intercepts equal to 1 and 2 on the x- and y-axes respectively. find the equation of the cirlce.
thanks in advance for your help

 

[pka]

This is what the question is looking for.
You can see the center.
What is the radius?

 

[stapel]

You can see the center.

But is a picture acceptable "proof" of this?

Another method:

The general equation of a circle is:

. . . . .x² + y² + Ax + By + C = 0

You are given that (0, 0), (1, 0), and (0, 2) are solutions of the above equation. Then:

. . . . .(0, 0): 0² + 0² + A(0) + B(0) + C = 0

So C = 0, and the equation for this circle may be simplified as:

. . . . .x² + y² + Ax + By = 0

Now plug in the other two points, and solve for A and B. This will give you the equation (in general form) for the circle. To find the center and radius, complete the square.

Eliz.

 

[pka]

But is a picture acceptable "proof" of this?
Eliz.

No of course not! But I assume that surely the student knows to find the intersection of perpendicular bisectors of the segments determined by the three non-collinear points.