[Math] Circles of radius $2$ passing through origin with centers on $x=1$

Question

There are two circles of radius $2$ that have centers on the line $x=1$
and pass through the origin. Find their equations.

Please explain to me what the problem is really saying.

Answer 1

Here is a small diagram representing question:

You have to find equations of circles.

There centres are $(1,\alpha) \ and (1,-\alpha)$ by symmetry .

And the radius is $2$ units.

let equation of circles are : $x^2+y^2-2x\pm2\alpha y=0$ [c=0; as circles pass through (0,0)] ; then $R=\sqrt{\alpha^2+1}=2$