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 } + 2*gx* + 2*fy* + 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

{ \left( x-a \right) }^{ 2 } + { \left( y-b \right) }^{ 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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