Find the radius and the center of the circle with the given equation x2+y2−6x−8y−30=0.

Center is (3,4)

Radius is √55 which is approximately 7.42

Step-by-step explanation:

First, recall the equation for a circle. The equation for a circle is given by:

Where (h,k) is the center and r is the radius.

We have the equation:

Thus, we want to turn this into the circle equation.

To do so, we need to complete the square.

First, put all the x-terms together and all the y-terms together. Also, add 30 to both sides:

Now, complete the square for both of the variables. Recall how to complete the square. If we have:

We divide b by 2 and then square it. Then we will have a perfect square trinomial. To keep things balanced, we must also subtract what we added.

Thus, for the first term:

And for the second term:

Replace the two terms:

Simplify. Add -9 and -16:

Add 25 to both sides:

This is now in the form of the circle equation.

Thus, the center is (3,4).

And the radius is √55 which is approximately 7.42

the balance is found at the link

step-by-step explanation:

they are simplified

step-by-step explanation: