Circle is one of the basic geometrical shape in mathematics. By definition, circle is nothing but the locus of all points situated at same distance from the center. To represent a circle, generally we are using equation. The equation is of two forms; **standard form and general form. **

**Standard form of circle equation** is,

where (a,b) is the center

r is the radius

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Circle Equation Calculator | Area of a Circle Formula Calculator |

Circumference of a Circle Formula Calculator | Quadratic Equation Formula Calculator |

Problems of circle equation are given below:

### Solved Examples

**Question 1: **If the center point and radius of a circle is given as (3, 5) and 4 respectively. Represent this as a circle equation ?

** Solution: **

Given parameters are

Center (a, b) = (3, 5); radius r = 4

The standard form of circle equation is,

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

So, $(x-3)^{2}$ + $(y-5)^{2}$ = $4^{2}$

So, $(x-3)^{2}$ + $(y-5)^{2}$ = 16

**Question 2: **Represent the given general form of a circle equation to standard form ?

x^{2 }+ y^{2 }- 2x - 4y - 4 = 0

** Solution: **

The given general form equation is,

x^{2} + y^{2} - 2x - 4y - 4 = 0

Take x terms together and y terms together

(x^{2} - 2x) + (y^{2} - 4y) = 4

Add (-1)^{2} on both sides

(x^{2} - 2x + (-1)^{2}) + (y^{2} - 4y) = 4 + (-1)^{2}

Add (-2)^{2} on both sides

(x^{2} - 2x + (-1)^{2}) + (y^{2} - 4y + (-2)^{2} ) = 4 + (-1)^{2} + (-2)^{2}

(x - 1)^{2} + (y - 2)^{2} = 9

Given parameters are

Center (a, b) = (3, 5); radius r = 4

The standard form of circle equation is,

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

So, $(x-3)^{2}$ + $(y-5)^{2}$ = $4^{2}$

So, $(x-3)^{2}$ + $(y-5)^{2}$ = 16

x

The given general form equation is,

x

Take x terms together and y terms together

(x

Add (-1)

(x

Add (-2)

(x

(x - 1)