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Equation of a Circle Formula

Circle is referred to a round shape boundary where all the points are equidistant from the centre. An equation is generally required to represent the circle. There are basically two forms of representation:

1. Standard Form
2. General Form

Standard Form of Circle Equation

\[\LARGE (x – a)^{2} + (y – b)^{2} = r^{2}\]

Where,
a, b is the center,
r is the radius

General form of Circle Equation

$\LARGE x^{2} + y^{2} + Ax + By + C = 0$

Solved Examples

Question 1: If the center point and radius of a circle is given as (4, 5) and 7 respectively. Represent this as a circle equation ?

Solution:

Given parameters are
Center (a, b) = (4, 5); radius r = 7
The standard form of circle equation is,
$(x-a)^{2}$ + $(y-b)^{2}$ = $r^{2}$
So, $(x-4)^{2}$ + $(y-5)^{2}$ = $7^{2}$
So, $(x-4)^{2}$ + $(y-5)^{2}$ = 49

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