## Equation of a Circle

The equation of a circle can be derived using Pythagoras Theorem. The circle below has centre
$(x_1,y_1)$
. 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,
$(x-x_1)^2+(y-y_1)^2=r^2$