write the equation of the equation with radius "a" and touching both axes geometry
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