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
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