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Equation of a Circle Formula

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,
Standard Circle Equation
where (a,b) is the center
           r is the radius
General form of circle equation is,
General Circle Equation

Related Calculators
Circle Equation Calculator Area of a Circle Formula Calculator
Circumference of a Circle Formula Calculator Quadratic Equation Formula Calculator
 

Equation of a Circle Problems

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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 ?
x2 + y2 - 2x - 4y - 4 = 0

Solution:
 
The given general form equation is,
x2 + y2 - 2x - 4y - 4 = 0
Take x terms together and y terms together
(x2 - 2x) + (y2 - 4y) = 4
Add (-1)2 on both sides
(x2 - 2x + (-1)2) + (y2 - 4y) = 4 + (-1)2
Add (-2)2 on both sides
(x2 - 2x + (-1)2) + (y2 - 4y + (-2)2 ) = 4 + (-1)2 + (-2)2
(x - 1)2 + (y - 2)2 = 9

 

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