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Draw a square of side 'b' taking PS as the axes. Now the co-ordinates of its vertices are `P(0,0), Q(b,0),R(b,b) and S(0,b)` <br> From the equation of circumcircle of square PQRS, <br> `(x_(1),y_(1))=(0,0) and (x_(2),y_(2))=(b,b)` <br> Equation of circle <br> `(x-x_(1))(x-x_(2))+(y-y_(1))(y-y_(2))=0` <br> `rArr (x-0)(x+b)+(y-0)(y-b)=0` <br> `rArr x^(2) -bx + y^(2) -by =0` <br> `rArr x^(2) +y^(2)=b(x+y)`. <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/NTN_MATH_XI_C11_S01_014_S01.png" width="80%">**Standard equation of circle**

**General Equation of Circle When the circle passes through the origin.**

**General Equation of Circle When the circle touch x axis and y axis .**

**General Equation of Circle When the circle touches both the axis.**

**Important points to remember**

**Find the Equation; radius; center of the circle and its x intercept and y intercept ?**

**Theorem:- Prove that the equation `x^2+y^2+2gx+2fy+c=0` always represent a circle whose centre is `(-g;-f)` and radius `sqrt(g^2+f^2-c)`**

**Diameter form of the circle**

**Parametric form of circle**

**Equation of a circle passing through 3 points**