Completing the Square/Finding Center & Radius of Circle

[TrueStar]

Homework Statement

Find the center and radius of the circle with the given equation:

x^2+y^2+4y-117=0

Homework Equations

Completing the Square

Formula of a Circle
(x-h)^2-(y-k)^2=r^2

The Attempt at a Solution

All of the problems I've encountered like this involve completing the square. I haven't seen one where there is no X and coefficient (the same goes for Y). I was able to correctly calculate that the y-coordinate of this circle is -2. The x-coordinate is supposed to be 0 and the radius is 11, but I don't know the steps to get there. I have no x coefficient to complete the square with.

Thank you!

 

[Mark44]

x^2+y^2+4y-117=0

All of the problems I've encountered like this involve completing the square. I haven't seen one where there is no X and coefficient (the same goes for Y). I was able to correctly calculate that the y-coordinate of this circle is -2. The x-coordinate is supposed to be 0 and the radius is 11, but I don't know the steps to get there. I have no x coefficient to complete the square with.

Not having an x term actually makes it easier. After all, x^2 = (x - 0)^2, right?

 

[symbolipoint]

x^2+y^2+4y-117=0, also commonly notated as
x² + y² + 4y - 117 = 0, may be rearranged to
x² + y(y + 4) - 117 =0,
x² + y(y + 4) = 117

The expression with 'y' can represent a rectangle with "length" y+4 and "height" of y. This rectangle can be itself rearranged to show a missing square section. The process of completing the square is the arithmetic addition of this missing square piece. When you add this square piece to complete the square, you must do so to both sides of the equation. The goal is to be able to set the equation into standard form; it was originally given in general form. Standard form permits you to easily graph the circle.

 

[TrueStar]

Yes, this makes sense. I still don't understand how the radius equals to 11 though..unless they rounded the square root of 113.

 

[Mark44]

No, they didn't round the square root of 113. How did you get 113?

You have x^2 + y^2 + 4y - 117=0
so x^2 + y^2 + 4y = 117

What do you have to add to the left side to complete the square? You need to add the same amount to the right side.

 

[TrueStar]

I'm sorry, I subtracted instead of added 4. Adding 4 to 117 is 121 and the square root of 121 is 11.

Thanks for explaining this everyone. It was much simpler than I made it out to be.

 

[snickersf12]

Find the standard form of the equation 16x^2+9y^2+64x-18y-71= 0

 

[Mark44]

You should start a new thread rather than highjack an existing thread.