# *Circle The locus of a point P (x, y) which moves in a plane so that its distance from a fixed point is always a

*Circle The locus of a point P (x, y) which moves in a plane so that its distance from a fixed point is always a constant. The fixed point is called the centre C (u, v) of the circle and the constant distance is called its radius (R).

Also a radius of a circle is a straight line joining the centre any point on the circumference. As CP = R, thus using displacement formula we can write

The above expression is called Central form of a circle.

A circle can also be expressed as

ax^{2} + by^{2} + 2 gx + 2 fy + c = 0

This expression is called general form of a circle.

Here (-g, -f) is the center of the circle

is radius

If centre of a circle coincides with origin O (0, 0) then the above expression can be written as,

x^{2 }+ y^{2 }= R^{2}. ^{ }

**This expression is called Standard form of a circle.**