Equation of a Circle





In this page equation of a circle we are going to see the methods to find the equation of any circle.Generally we have three ways to find the equations.The methods to be used is depending on the information given in the question.

First let us consider the definition of a circle.

A circle is the locus of a point which moves in such way that its distance from a fixed point is always constant.This fixed point is called the center of a circle and a distance from the center is called the radius. 

Here O is the center of the circle and distance from O to A is called the radius of the circle and it is denoted by "r". Generally we can find the equation of a circle in two ways.

(1) Equation of the circle when the center and the radius are given

(2) Equation of the circle if the end points of a diameter are given

Equation of the circle when the center and the radius are given:

For using the first method we must need the center and the radius of a circle.Here we have to consider the center as (h,k) and radius as "r". Let us see the formula to be used in this method

(x-h)² + (y-k)² = r² 

If the center of a circle is (0,0) then the equation of circle will be in the form of x² + y² = r².Because here the value of (h,k) is (0,0).

Equation of the circle when the end points of a diameter are given:

Let A(x₁,y₁) and B(x₂,y₂) be the end points of the diameter.The the equation of circle will be

(x-x₁) (x-x₂) + (y-y₁) (y-y₂) = 0

General Equation of the circle

x² + y² + 2gx + 2fy + c = 0

Some times we will have a equation in the form of above equation and we will be asking to find the center and the radius of a circle.That time we have to consider the center of a circle as (-g,-f) and radius of a circle as √g² + f² - c.

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