Equation of a Circle - College Level

Find the center and radius of the circle that is determined by the following equation:

Answer :
Center = (4,-3)
Radius = 6

The solution is shown step by step below. A detailed description of the solution is provided below the equations.

The problem requires that you find the values for (h , k) and the radius. In order to do that you must first solve for x and y to be able to find the radius points.

You start the problem by making sure that the similar variables are grouped together as follows:

It is noted here that in order to move the number 11 to the other side of the equation, we must first add 11 to both sides of the equation.

You must rework the problem to bring it to the standard form of the equation of the circle. Which is:

In order to do that we must complete the square inside each bracket to find the missing values. We must complete the square for x and for y in order to come up with two quadratic equations that we can factor.

We’ll start with x :
The way to complete the square is by taking half the middle value (number) of the quadratic equation, squaring it and adding it to both sides of the equation.

In this case, the middle value is 8 so we take half of 8, which is 4, and square it so we get 16. This number (16) is added to both sides of the equation as follows:

Now we do y:
The way to complete the square is by taking half the middle value (number) of the quadratic equation, squaring it and adding it to both sides of the equation.

In this case, the middle value is 6 so we take half of 6, which is 3, and square it so we get 9. This number (9) is added to both sides of the equation. The resulting equation looks like this:

Now we have two quadratic equations that can be factored. Once they are factored we end up with the following equation:

At this point, it is feasible to solve for x and y by setting each factor to 0 and solving for the variable we come up with:
X = 4
Y = -3

Once we have solved for x and y, it means we found our h and k values which in this case comes out to be (-3,-4).

We still need to find the radius. Since we added a 9 and a 16 to the 11 on the right side of the equation that means we added a total of 36 to the right side of the equation. This 36 is the square of the radius.

If we take the square root of 36 we come up with 6, which is our radius.

Now we have solved the equation and are results are:

(4 , -3) , 6



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