Different Forms of Equations of Circle

The collection of all points in a plane that are at a fixed distance from a fixed point in the plane is called a circle. The fixed point is called the centre and the constant distance is called the length of the radius of the circle. The length of the longest chord in a circle that also passes through its centre is called its diameter. A circle divides the plane into three parts, i.e., the interior, the circle and the exterior.

The equation of a circle is calculated in three forms:

    The standard equation of the circle (also known as centre-radius form of equation of circle)

    The general equation of the circle

    Diameter form of equation of circle

An equation of a circle contains three independent arbitrary constants. The circle is completely determined if we know the values of these three constants.

To know the values, we require three conditions about the circle. These can be any geometric conditions such as:

    Three given points through which the circle passes

    Two given points on the circle and a line on which the centre lies.

    Centre and a point on circle

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