OUR SOLUTION OF PROBLEM: 1

QUESTION : Find the equation of the circle touching the axes and having radius of 1 unit.

SOLUTION:

Since the required circle is touching both the axes, the coordinate of the centre of circle will be in the form of (r,r) where r is the radius of circle.
So the eq. of circle will be (x-r)sq +(y-r)sq = r sq
but here we can have in total 4 such circles
Having centre at (+-r, +-r)

Each of these circle will be 4 different quadrant.
In the given problem r=1
So the eq of circles will be
(x-1)sq +(y-1)sq = r sq Ist quadrant circle
(x+1)sq +(y-1)sq = r sq IInd quadrant circle
(x+1)sq +(y+1)sq = r sq IIird quadrant circle
(x-1)sq +(y+1)sq = r sq IVth quadrant circle