## Equation of a Circle

\[(x_1,y_1)\]

. The point \[(x,y)\]

lies on the circle.Construct a right angled triangle with hypotenuse from the centre

\[(x_1,y_2)\]

to the point \[(x,y)\]

- and so equal to the radius \[r\]

of the circle, base parallel to the \[x\]

- axis and height parallel to the \[y\]

- axis.Then the base of the triangle is

\[x-x_1\]

and the height is \[y-y_1\]

.From Pythagoras Theorem,

\[(x-x_1)^2+(y-y_1)^2=r^2\]