Understanding the Standard Form of a Circle Equation | How to Represent and Calculate Circles in Cartesian Coordinates

standard form of a circle

The standard form of a circle is a way to represent the equation of a circle in Cartesian coordinates

The standard form of a circle is a way to represent the equation of a circle in Cartesian coordinates. It is written as:

(x – h)^2 + (y – k)^2 = r^2

where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle.

In this form, (x – h) and (y – k) represent the horizontal and vertical distances from any point (x, y) on the circumference of the circle to the center (h, k). When these distances are squared and added together, they should be equal to the square of the radius r.

To use the standard form, you need the values of the center coordinates (h, k) and the radius r. By substituting these values into the equation, you can create an equation that represents a circle on a coordinate plane.

For example, if a circle has its center at (2, -3) and a radius of 5 units, the standard form equation would be:

(x – 2)^2 + (y + 3)^2 = 25

This equation represents all the points that are equidistant from the center (2, -3) by 5 units, forming a circle with a radius of 5 units.

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