In Exercises 31–40, write the standard form of the equation of the circle with the given center and radius. Center (0, 0), r = 7

Verified step by step guidance

1. Identify the standard form of the equation of a circle, which is $(x-h{)}^2+(y-k{)}^2=r^2$, where $(h,k)$ is the center and $r$ is the radius.
2. Substitute the given center $(0,0)$ into the equation, replacing $h$ with 0 and $k$ with 0.
3. Substitute the given radius $r=7$ into the equation.
4. Square the radius $r$ to find $r^2$.
5. Write the equation in standard form using the substituted values.

Key Concepts

Standard Form of a Circle's Equation

The standard form of a circle's equation is given by (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. This formula allows us to represent a circle in a Cartesian coordinate system, making it easier to identify its properties such as position and size.

Center of a Circle

The center of a circle is the point from which all points on the circle are equidistant. In the equation, it is represented by the coordinates (h, k). For the given problem, the center is at (0, 0), indicating that the circle is centered at the origin of the coordinate plane.

Radius of a Circle

The radius of a circle is the distance from the center to any point on the circle. It is a crucial component in defining the size of the circle. In this case, the radius is given as 7, which means that every point on the circle is 7 units away from the center (0, 0).