An equation of a circle is x2 + y2 + 10x – 6y + 18 = 0. Show all your work in determining the center and radius of this circle. In complete sentences, explain the procedure used.

Question

apoorvk · Answer

Hey complete squares in 'x' and 'y'.

anonymous · Answer

I dont know how?

apoorvk · Answer

Now, when you complete squares, you will get the equation in the form of:
$$(x-a)^2 + (y-b)^2 = r^2$$

Here, (a,b) would be the center and 'r' the center.

anonymous · Answer

ok? but i dont know how to do that!

terenzreignz · Answer

First, put the x's and y's together:
$$x^{2} +10x + y^{2} - 6y +18 = 0$$
I'll show you how to complete the square for the 'x' part, you do the same for the 'y'

Let's only look at the x's for now:
$$x^{2} + 10x$$
What we do is we take the term with just the x (not x squared) and look at its coefficient, which happens to be 10 (whether or positive or negative is unimportant, at this point)
Now pay attention to this:
We take that coefficient (10), we divide it by two (5) and then square it (25)
Now that we have that, we ADD it to this expression to get
$$x^{2} + 10x + 25$$
BUT, we have changed the expression by adding 25, to make sure it's the same expression, we also subtract 25, like so:
$$x^2 + 10x + 25 -25$$
Look at the first three terms.... As you can see, it is a PERFECT SQUARE TRINOMIAL, so this can be written as
$$(x^2 + 10x + 25) -25$$
$$(x + 5)^{2} - 25$$
And that's how you complete the square, now try doing that with the 'y' part 

:D