In Exercises 31–40, write the standard form of the equation of the circle with the given center and radius. Center (-1, 4), r = 2

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, making it fundamental for graphing and analyzing circles in coordinate geometry.

Coordinates of the Center

The center of a circle is represented by the coordinates (h, k). In this case, the center is given as (-1, 4), meaning the circle is located at the point where x = -1 and y = 4 on the Cartesian plane. Understanding how to interpret these coordinates is essential for correctly applying them in the standard form equation.

Radius of a Circle

The radius of a circle is the distance from the center to any point on the circle. It is denoted by r and is crucial for determining the size of the circle. In this problem, the radius is given as 2, which means that the circle extends 2 units in all directions from its center, affecting the equation's right side in the standard form.