The equation for a circle of radius  centered on point  has the equation 

Just as with linear equations, the horizontal and vertical shifts are opposite of their sign, and are inside the parentheses. The equation of a circle simply must be memorized.

So the circle is centered on point , and plug those in and it yields the formula of the circle.

First determine the center of the circle. The "x-3" portion of the circle equation tells us that the x coordinate is equal to 3. The "y-3" portion of the circle equation tells us that the y coordinate is equal to 3 as well. Therefore, the center of the circle is at (3,3).

To find the distance between (3,3) and (0,0), it is necessary to use the Pythagorean Theorem . Where "a" and "b" are equal to 3

(to visualize, you may draw the two points on a graph, and create a triangle. The line connecting the two points is the hypotenuse, aka "c." )

Write the standard form for the equation of a circle.

The value of  is  and the value of  is .  The center of the circle is:

To find the radius, set  and solve for .

Take the square root of both sides. We only consider the positive value since distance cannot be negative.

The answer is:  

Recall that the standard equation of a circle is . Therefore, in this case . Square root both sides to find your radius. can be simplified to , which is your answer.

First, recall what the standard equation of a circle: . Your center is (h,k). Remember to flip the signs to get your center for this equation: .

Recall what the standard equation of a circle is:

.

is the center of the circle.

Remember that you have to change the signs!

Thus, since our equation is,

your answer for the center is: .

Recall that the standard equation of a circle is

.

Therefore, looking at the equation given,

.

Solve for r to get 7.

Step 1: Recall the general formula of a circle with a center that is not at .

, where  is the center.

Step 2: Find the value of h and k here..

. To find this, we set  of the general equation equal to   (which is in the question)

. To find this, we set  equal to .

The vertex is .

Step 3: To find the radius, take the square root of .

In the equation, we will get .

The radius of the circle is 

The equation of a circle is in the format:

where  is the center and  is the radius.

Multiply two on both sides of the equation.

The equation becomes:

The center is .

The radius is .

The answer is:  

To rewrite the given function as the equation of a circle in standard form, we must complete the square for x and y. This method requires us to use the following general form:

To start, we can complete the square for the x terms. We must halve the coefficient of x, square it, and add it to the first two terms:

Now, we can rewrite this as a perfect square, but because we added 4, we must subtract 4 as to not change the original function:

We do the same procedure for the y terms:

Rewriting our function, we get

Moving the constants to the right side, we get the function of a circle in standard form:

Comparing to

we see that the radius of the circle is

Notice that the radius is a distance and can therefore never be negative.