# Equation of a Circle Touching Both Axes

In this tutorial we find the equation of circles with both axes touching, i.e. the X-axis and Y-axis, with any given radius. So we will find the equation of a circle in all four quadrants.

Let the equation of the required circle having a center and radius be

In the first quadrant, the equation of a circle can be found by using center ${C_1}\left( {r,r} \right)$ and the radius is equal to $r$, so equation (i) becomes

In the second quadrant, the equation of a circle can be found by using center ${C_2}\left( { - r,r} \right)$ and the radius is equal to $r$, so equation (i) becomes
In the third quadrant, the equation of a circle can be found by using center ${C_3}\left( { - r, - r} \right)$ and the radius is equal to $r$, so equation (i) becomes
In the forth quadrant, the equation of a circle can be found by using center ${C_4}\left( {r, - r} \right)$ and the radius is equal to $r$, so equation (i) becomes