Final answer:
The standard equation of a circle with center at the origin and radius 7 is x^2 + y^2 = 7^2.
Step-by-step explanation:
The standard equation of a circle with center at the origin and radius 7 is given by the formula:
x^2 + y^2 = 7^2
where x and y are the coordinates of a point on the circle.
For example, if we substitute x = 3 and y = 4 into the equation, we can check if the point (3, 4) lies on the circle. 3^2 + 4^2 = 25, which is equal to 7^2.