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# What is the general form of the equation of a circle with center at (a, b) and radius of length m?

x^{2} + y^{2} - 2ax - 2by + (a^{2} + b2 - m^{2}) = 0.

x^{2} + y^{2} + 2ax + 2by + (a^{2} + b2 - m^{2}) = 0.

x^{2} + y^{2} - 2ax - 2by + (a^{2} + b^{2} + m^{2}) = 0.

x^{2} + y^{2} + 2ax + 2by + a^{2} + b^{2} = -m^{2}.

**Solution:**

Given center (a, b) and radius 'm'

The equation of circle provides an algebraic way to describe a circle given with its center and radius.

We have the standard equation (x - a)^{2} + (y - b)^{2} = m^{2}

By expanding this we get,

x^{2} - 2ax + a^{2} + y^{2} - 2by + b^{2} = m^{2}

x^{2} + y^{2} - 2ax - 2by + a^{2} + b^{2} - m^{2} = 0

It is given by x^{2} + y^{2} - 2ax - 2by + (a^{2} + b^{2} - m^{2}) = 0

## What is the general form of the equation of a circle with center at (a, b) and radius of length m?

**Summary:**

The general form of the equation of a circle with center at (a, b) and radius of length m is x^{2} + y^{2} - 2ax - 2by + (a^{2} + b^{2} - m^{2}) = 0.

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