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Circle

6

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)= 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)= 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)= 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)= h2 
                  OR,
→(x-k)2+(y-k)= k2 
                  OR,
→(x-r)2+(y-r)= 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