How to solve and graph equations of cirlces

In order to graph an equation of a circle we must first understand how to come up with the standard form of an equation of a circle. We can find this equation by thinking about the Pythagorean theorem, and how we manipulate it to find the distance formula and now we are going to use that same idea to find the standard form of an equation of a circle.

Example of standard form of a circle: $${ (x-h) }^{ 2 }+{ (y-k) }^{ 2 }=r^{ 2 }$$

Once you get used to the standard form of the equation it's important for you to than be able to get to the general form the equation.

You can get back to the general form by foiling out the standform the equation of a circle

Example of general form of a circle: $${x^2+y^2+ax+by+c=0}$$

The last part now is to get back to the standard form of the equation.

You can get back to the standard form by completing the square of the equation.

$${ x }^{ 2 }+x+n +{ y }^{ 2 }+y+n= n$$