# Find the center and the radius from the equation

A circle is the collection of points that are equidistant to a center point.  The distance is the radius denoted r.  The center is denoted .

The standard form of an equation of a circle is where r is the radius and   is the center.

Example:  Find the center and the radius from the given equation.

Solution:  If you line up the standard form of a circle with the equation given you can determine the center and the radius.

In the binomial with x, the number after the minus sign is h.  Thus, .  In the binomial with y, the number after the minus sign is k.  Thus, .  The lines up with 16.  So which means .

This is the equation of a circle with a center of and a radius of .

Example:  Find the center and the radius from the given equation.

Solution:  Notice that one of the binomials has a + instead of the – that is in the standard form of the circle.  Rewrite the addition as subtraction.

is the same as .

The rewritten equation is as follows.

Then, if you line up the standard form of a circle with the equation given you can determine the center and the radius.

In the binomial with x, the number after the minus sign is h.  Thus, .  In the binomial with y, the number after the minus sign is k.  Thus, .  The lines up with 25.  So which means .

This is the equation of a circle with a center of and a radius of .

Example:  Find the center and the radius from the given equation.

Solution:  Notice that one of the binomials has a + instead of the – that is in the standard form of the circle.  Rewrite the addition as subtraction.

is the same as .

The other binomial doesn’t have any number added or subtracted.  We can rewrite this by subtracting zero.

is the same as .

The rewritten equation is as follows.

Then, if you line up the standard form of a circle with the equation given you can determine the center and the radius.

In the binomial with x, the number after the minus sign is h.  Thus, .  In the binomial with y, the number after the minus sign is k.  Thus, .  The lines up with 25.  So which means .

This is the equation of a circle with a center of and a radius of .