What is the general form of the equation of a circle with center at (a, b) and radius of length m?
x² + y² - 2ax - 2by + (a² + b2 - m²) = 0.
x² + y² + 2ax + 2by + (a² + b2 - m²) = 0.
x² + y² - 2ax - 2by + (a² + b² + m²) = 0.
x² + y² + 2ax + 2by + a² + b² = -m².

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 = m²

By expanding this we get, 

x² - 2ax + a² + y² - 2by + b² = m²

x² + y² - 2ax - 2by + a² + b² - m² = 0

It is given by x² + y² - 2ax - 2by + (a² + b² - m²) = 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 x² + y² - 2ax - 2by + (a² + b² - m²) = 0.