Circle

1. When the center of circle is origin.

→x²+y² = r²

2. When the center of circle is (h, k).

→(x-h)²+(y-k)² = r² ..................(i)

3. When the circle touches x-axis.

If the circle touches x-axis then, r=k and putting the value in equation (i)
→(x-h)²+(y-k)² = k² 

4. When the circle touches y-axis.

If the circle touches y-axis then, r=h and putting the value in equation (i)
→(x-h)²+(y-k)² = h² 

5.When the circle touches both axes.

If the circle touches both axes then, r=h=k and putting the value in equation (i)
→(x-h)²+(y-h)² = h² 
                  OR,
→(x-k)²+(y-k)² = k² 
                  OR,
→(x-r)²+(y-r)² = r² 

6. When the circle passes through origin.
 
If the circle passes through origin then, r²=h²+k² and putting the value in equation (i)
→(x-h)²+(y-k)²= h²+k²