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

1 Answer
Jul 25, 2016

Answer:

The family of circles touching both the axes in any of the four quadrants is given by #f(x, y, a) = x^2+y^2+-2ax+-2ay+a^2=0#.

Explanation:

If the radius is a, the center of the circle will be at #(+-a, +-a)#.

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

circle lies..

So, the equation is

#f(x, y, a) = (x+-a)^2+(y+-a)^2-a^2#

#=x^2+y^2+-2ax+-2ay+a^2=0#.

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