# How do you write the equation for a circle with radius a and touching both axes?

Jul 25, 2016

The family of circles touching both the axes in any of the four quadrants is given by $f \left(x , y , a\right) = {x}^{2} + {y}^{2} \pm 2 a x \pm 2 a y + {a}^{2} = 0$.

#### Explanation:

If the radius is a, the center of the circle will be at $\left(\pm a , \pm a\right)$.

The four pairs of signs is indicative of the quadrant in which the

circle lies..

So, the equation is

$f \left(x , y , a\right) = {\left(x \pm a\right)}^{2} + {\left(y \pm a\right)}^{2} - {a}^{2}$

$= {x}^{2} + {y}^{2} \pm 2 a x \pm 2 a y + {a}^{2} = 0$.

'a' is the parameter. for this family of circles f(x, y, a) = 0..