The equation of a circle is , in which (h, k) is the center of the circle. To derive the center of a circle from its equation, identify the constants immediately following x and y, and flip their signs. In the given equation, x is followed by -1 and y is followed by -6, so the coordinates of the center must be (1, 6).

To convert the given equation into the format , complete the square by adding to the x-terms and to the y-terms.

The square root of 4 is 2, so the radius of the circle is 2.

Look at the formula for the equation of a circle below.

Here is the center and is the radius. Notice that the subtraction in the center is part of the formula. Thus, looking at our equation it is clear that the center is and the radius squared is . When we square root this value we get that the radius must be .

The equation of a circle is , in which (h, k) is the center of the circle and r is its radius. Because the graph of the circle is centered at (2, -3), h and k are -2 and 3. Because the radius is 4, the right side of the equation is equal to 16.

The equation of a circle is , in which (h, k) is the center of the circle and r is its radius. Because the graph of the circle is centered at (0, 0), h and k are both 0. Because the radius is 3, the right side of the equation is equal to 9.

To convert the given equation into the format , complete the square by adding to the x-terms and to the y-terms.

The square root of 25 is 5, so the radius of the circle is 5.

The equation of a circle in standard for is:

Where the center and the radius of the cirlce is .

Dividing by 4 on both sides of the equation yields

or

an equation whose graph is a circle, centered at (2,3) with radius = .5

Rewrite the equation of the circle in standard form

as follows:

Since and , we complete the squares by adding:

The standard form of the equation sets

,

so the radius of the circle is

The equation can be rewritten so that it looks like the parent equation for a circle . After completeing the square, the equation changes from to . From there it can be expressed as . Therefore the center of the circle is at .

The parent equation of a circle is represented by . The radius of the circle is equal to . The radius of the cirle is .