Understanding the Standard Form Equation of a Circle | Center, Radius, and Geometric Properties

standard form of a circle

The standard form of a circle is an equation that describes the geometric properties of a circle on the Cartesian plane

The standard form of a circle is an equation that describes the geometric properties of a circle on the Cartesian plane. It is written in the form:

(x – h)^2 + (y – k)^2 = r^2

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

To write an equation in standard form, you need to know the center and the radius of the circle.

For example, if the center is at (2, -3) and the radius is 5, the equation in standard form would be:

(x – 2)^2 + (y + 3)^2 = 5^2

Simplifying this equation, we get:

(x – 2)^2 + (y + 3)^2 = 25

The standard form equation allows us to easily identify the center and radius of a circle and understand its geometric properties.

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