The standard form for the equation of a circle with the center at the origin is:
x² + y² = r²
Given that the radius is 7, we can easily generate the equation of the circle by plugging in the value of r into the equation. So,
x² + y² = 7²
x² + y² = 49
Therefore, the equation of the circle with its center at the origin and with radius of 7 is
x² + y² = 49