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.

When identifying the center of a circle, take the opposite sign of each value connected to x and y. 

The equation given represents a circle.

 represents the center, and  is the radius.

The center is at:  

Set up an equation to solve the radius.

The radius is:  

The answer is:  

Write the standard form for a circle.

The circle is centered at:  

The radius is:  

Substitute all the known values into the formula.

Simplify this equation.

The answer is:  

First, we need to become familiar with the standard form of a hyperbolic equation:

The center is always at . This means that for this problem, the numerators of each term will have to contain and .

To determine if a hyperbola opens vertically or horizontally, look at the sign of each variable. A vertical parabola has a positive term; a horizontal parabola has a positive term. In this case, we need a vertical parabola, so the term will have to be positive.

(NOTE: If both terms are the same sign, you have an ellipse, not a parabola.)

The asymptotes of a parabola are always found by the equation , where  is found in the denominator of the term and is found in the denominator of the term. Since our asymptotes are , we know that must be 4 and must be 3. That means that the number underneath the term has to be 16, and the number underneath the term has to be 9.

The standard equation of a hyperbola is: