The standard form of the equation of a circle is expressed as:
(x – h)² + (y – k)² = r²
In this equation:
- (h, k) represents the center of the circle.
- r represents the radius of the circle.
To break it down further, the expression (x – h)² + (y – k)² shows the distance of any point (x, y) on the circle from the center (h, k). The equation states that the sum of the squares of these horizontal and vertical distances must equal the square of the radius (r).
For example, if you have a circle centered at (3, -2) with a radius of 5, the equation would look like:
(x – 3)² + (y + 2)² = 25
This means that any point (x, y) that satisfies this equation lies on the circumference of the circle. Understanding this form is crucial for graphing circles and solving related mathematical problems.