Answer:
A circle centered at the origin (0,0) can be represented by the equation (x-0)^2 + (y-0)^2 = r^2, where r is the radius of the circle.
Given that the circle is passing through the point (6,0), we can use this point to find the radius of the circle. The distance between the center of the circle (0,0) and a point on the circle (6,0) is the radius of the circle.
We can use the distance formula to find the radius:
r = √((x2-x1)^2 + (y2-y1)^2)
where (x1,y1) is the center of the circle and (x2,y2) is a point on the circle.
Plugging in the values:
r = √((6-0)^2 + (0-0)^2) = √(6^2) = √36 = 6
Therefore, the equation of the circle centered at the origin and passing through the point (6,0) is (x-0)^2 + (y-0)^2 = r^2, where r is 6.
So the equation of the circle is: x^2 + y^2 = 36.