What does it mean when we say circle is passing through origin?

Question

i can imagine a line passing through the origin in infinite ways but circle is not a line and i am unable to picture it in my brain. i mean its a round figure not a line and its centre can be anywhere near the origin so what does it actually mean? does it touch both the coordinate axis? which should mean origin (0, 0) is inside the circle? in most websites and books they just start solving a problem when it touches x or y but dont clear this.

Answer 1

A circle passing through the origin means that the origin, i.e., the point $(0,0)$, lies on the circle.

In other words, $(0,0)$ satisfies the equation of the circle.

Answer 2

Take a circle. Now mark a point $P$ on its circumference. It is a circle passing through the point $P$. If that point $P$ can be chosen to be origin, well and good. Now take any point on the plane. Let its distance from origin be $r$ units. With that point as centre a circle of radius $r$ will be passing through origin.