61. Write the general equation of a sphere whose center coincides with the origin. Write the general equation of a sphere passing through the origin and with its center on the $O x$ axis.
61. When $a=b=c=0$ we get: $x^{2}+y^{2}+z^{2}=R^{2}$. If the center of the sphere passing through the origin lies on the $O x$ axis, then the coordinates $(a, b, c)$ of the center are $a=R, b=0, c=0$ and the equation of the sphere takes the form:

$$
x^{2}-2 R x+y^{2}+z^{2}=0
$$