Circle

The locus of a closed curve of a moving point which moves in a plane in such a way that the distance from the fixed point to it is always constant is called circle. The constant distance is called radius and the fixed point is called the Centre.

 Equation of Circle

1.   Equation of the circle with centre at (0, 0) and radius r: x2 + y2 = r2.

2.   Equation of the circle with centre at (h, k) and radius r: (x – h)2 + (y – k)2 = r2. 

3.   The equation of the circle in the diameter form with its ends of diameter (x1, y1) and (x2, y2):

      (x – x1) (x – x2) + (y – y1) (y – y2) = 0.

4.   If the circle with centre at (h, k) and radius r touches both the axes then h = k = r.

5.   If the circle with centre at (h, k) and radius r touches x–axis, then k = r.

6.   If the circle with centre at (h, k) and radius r touches y–axis, then h = r. 

 Solved Examples