Equation of a Circle – Standard Form

What is the equation of the Circle?

In this tutorial we will discuss what is an equation of a circle formula in standard form and find the equation of a circle with examples.

First we know what is a circle ?

A circle is a set of all points which are equally distance from a fixed point in a plane.

The fixes point is called the center of the circle. The distance between any point on the circumference is called the radius of the circle.

An equation of a circle represents the position of a circle in Cartesian plane.

If we know the coordinates of the center of the circle and the length of its radius, we can write the equation of the circle. The equation of the circle represents all points that lie on the circumference of the circle. The standard form of equation of a circle is easier to understand and read.

Standard Form of a circle A circle without touching any axis of the two dimensional cartesian cordinate system is a standard equation is called the equation of a circle in standard form.

The standard form of equation of a circle is given by:(x-h)² + (y-k)² = r

Where (h, k) is the coordinates of the circle and r is radius and (x, y) is the arbitrary coordinates on the circumference of the circle.

This is the standard form of the equation. thus if we know the radius and coordinates of the center of the circle we can easily find its equation.

Example: Point (2, 3) is the center of the circle and radius is equal to 5 cm.

Then the equation of the circle will be:

(x – 2)² + (y – 3)² = 5²

(x² – 4x + 4) + (y² – 6y + 9) = 25

x² + y² – 4x – 6y + 4 + 9 = 25

x² + y² – 4x – 6y + 13 = 25

x² + y² – 4x – 6y = 25 – 13

x² + y² – 4x – 6y = 12

x² + y² – 4x – 6y – 12 = 0

which is called the standard form for the equation of a circle.