Equation of a Circle

A circle is a set of points in a plane that are equidistant from a fixed point called the center. The equation of a circle in the Cartesian plane is represented by the formula:

(x - h)² + (y - k)² = r²

Where:

• (h, k) are the coordinates of the center of the circle
• r is the radius of the circle
• (x, y) are the coordinates of any point on the circle

This equation essentially states that the distance between the center of the circle (h, k) and any point (x, y) on the circle is equal to the radius (r) of the circle.

Example:

If we have a circle with a center at (3, 4) and a radius of 5, the equation of the circle would be:

(x - 3)² + (y - 4)² = 5²

Which simplifies to:

(x - 3)² + (y - 4)² = 25

Thus, this equation represents a circle with a center at (3, 4) and a radius of 5.