Do you know that any circle can be represented by an equation? Now we will learn the **equation of a circle** and its various forms. You should understand its importance in exams. If you are attempting any competitive exams then definitely you have to learn about **circle equations**. Not only equations we have some other concepts on the circle. But right now we will concentrate on equations of the circle. Remaining topics associated with a circle I will discuss later.

We know that a straight line can be represented by a linear equation. And also we studied different forms straight line equations in coordinate geometry. In the same way, we can represent a **circle** by an equation. Like straight lines, a circle equation can be also represented in **different forms**. Now we will list out all the equations one by one.

**The Equation of a circle in various forms:**

**»General form:**

X^{2} + y^{2} + 2gx + 2fy + c = 0 is equation of circle with centre (-g, -f) and radius r = square root of g^{2} + f^{2} – c

**»Diameter form:**

Let us consider a circle with centre C and let P ( x_{1 , }y_{1}) and Q ( x_{2 , }y_{2}) be any two points on a circle. Then the equation of a circle is given as

(y – y_{1}) (y – y_{2}) + (x – x_{1}) (x – x_{2}) = 0

**»Centre – radius form:**

Let

The centre of a circle be (a, b) and radius of the circle be represented by the letter “r” then the **equation of a circle** is given by

(x-a)^{ 2} + (y-b)^{ 2} = r^{2 }

**»Parametric form:**

Let us consider the circle with centre C (a, b), radius r and let α be the parameter. Then the coordinates of any point on the **circle** will be of the form (a + r cosα, b + r sinα ).

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