In Exercises 31–40, write the standard form of the equation of the circle with the given center and radius. Center (−3, −1), r = √3

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 format allows for easy identification of the circle's center and radius, facilitating graphing and analysis.

Coordinates of the Center

The center of a circle is represented by the coordinates (h, k). In this case, the center is given as (−3, −1), meaning the circle is located 3 units left and 1 unit down from the origin. Understanding the center's coordinates is crucial for accurately placing the circle on a coordinate plane.

Radius of a Circle

The radius of a circle is the distance from the center to any point on the circle. In this problem, the radius is given as r = √3, which indicates that the circle extends √3 units from its center in all directions. Knowing the radius is essential for determining the size of the circle and completing its equation.