# 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:**

In the first quadrant, the equation of a circle can be found by using center and the radius is equal to , so equation (i) becomes

**In the Second Quadrant:**

In the second quadrant, the equation of a circle can be found by using center and the radius is equal to , so equation (i) becomes

**In the Third Quadrant:**

In the third quadrant, the equation of a circle can be found by using center and the radius is equal to , so equation (i) becomes

**In the Forth Quadrant:**

In the forth quadrant, the equation of a circle can be found by using center and the radius is equal to , so equation (i) becomes