Using the distance formula, the diameter is 10 units long, so the radius is 5.  Then, by finding the midpoint of the diameter, you know the center of the cirle.  Plugging values into the circle equation yields the final answer.

The equation for a circle is  where the center of the circle lies at the point  and the radius of the circle is . If we are looking for a circle with a diameter of , then its radius must be . For the circle to be tangent to the x-axis at the point  and the y-axis at , it must be centered at the point . Therefore, the equation of the circle will be .

The equation for a circle is

where (h, k) is the center of the circle and r is the radius.

Plugging in the values of , , and , we get

The formula for the equation of a circle is:

The values of  represent the center, and both values are zero at the origin.

Plug in the known values and reduce.

The domain of a circle gives the width of the circle, the range of a circle gives the height of a circle - both of which equal the diameter. 

The domain and range numbers are both 6 apart, meaning that the diameter of the circle is 6, which means the radius of the circle is 3. 

The halfway point between the domain gives the x-coordinate for the center of the circle, which in this case is 5. 5 is halfway between 2 and 8. 

The halfway point between the range gives the y-coordinate for the center of the circle, which in this case is 2. 2 is halfway between -1 and 5. 

Now we have all of the information needed to plug into the equation for a circle in standard form as shown below where r is the radius and the center is (h,k): 

Given a circle with radius of 3, and center of (5,2) we get the below equation of a circle. 

To determine the equation for a circle, we need to know the center and the radius. In this case, we know the center and one of the points on the circle. The radius of the circle is the distance from the center to this point, so to determine it, use the distance formula:

The equation for a circle is written as where the center is and the radius is r. For this circle, plug in and :

or more simply

To determine the equation of the circle, we need to know the radius, or the distance from the origin to the point on the circle. Use the distance formula:

Since the circle is centered at the origin, its equation is or more simply

Plugging in the point shows that this point is inside the circle, since the left side of the equation will be less than the right: 

The equation for a circle is in the form where is the center and r is the radius.

In this case:

The equation of a circle is defined by where the center is and the radius is r. The radius is the distance from the center to any point on the circle, so we can use the distance formula to calculate it:

The equation is then or more simplified,