write the equation of the equation with radius "a" and touching both axesgeometry

We have to determine the equation of the circle that has a
radius a and touches both the axes.

This is possible if the
center lies on the line x = y.

Also the distance of the
center from the x-axis and the y-axis is equal to the radius or
a.

Therefore the center is the point ( a,
a)

The general equation of a circle with center (a, b) and
radius r is given by (x - a)^2 + (y - b)^2 =
r^2

Substituting the values we have
here:

(x - a)^2 + (y - a)^2 =
a^2

=> x^2 + a^2 - 2ax + y^2 + a^2 - 2ay =
a^2

=> x^2 + y^2 - 2ax - 2ay + a^2 =
0

The required equation of the circle is x^2
+ y^2 - 2ax - 2ay + a^2 = 0