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


Practise This Question

DIRECTIONS : Match Column-I with Colum-II and select the correct answer using the codes given below the columns.
ColumnIColumnIIA. Electric motorP. Electrical energy to sound energyB. Electric bellQ. Electrical energy to mechanical energyC. Electric bulbR. Light energy to electrical energyD. Photoelectric cell energyS. Heat energy to mechanicalE. Steam engineT. Electric energy to light energy