Question

What is the standard form of the equation of the circle x2 -4x + y2 + 6y - 12 = 0?
Please help :)

Answer 1

you're going to have to complete the square on this eventually to find the proper equation, but first we need to move the 12 over to the other side of the = sign.

Answer 2

\[(x ^{2}-4x)+(y ^{2}+6y)=12\]

Answer 3

now you have to complete the square on the x terms and on the y terms. Do you know how to do that?

Answer 4

no I'm kind of new at this :)

Answer 5

For the x's: take half the x term (the x term is -4, half of that is -2) and square it to get (-2)^2 = 4. Add the 4 into the parenthesis by the x's and also add it to the 12 on the other side of the equals sign in order to keep the equation in balance. Like this:

Answer 6

\[(x ^{2}-4x+4)+(y ^{2}+6y)=12+4\]

Answer 7

That's the x terms. Now let's do the y terms in the exact same way. The y term has a coefficient of 6 on it. Half of 6 is 3, and squaring the 3 gives you 9. So we add that in the parenthesis by the y's and also on the other side by the 12 and the 4. Like this:

Answer 8

\[(x ^{2}-4x+4)+(y ^{2}+6y+9)=12+4+9\]

Answer 9

We can easily add the numbers on the right side of the equals sign together to get 25 (which happens to be a nice squared number!). As for the left side...

Answer 10

Within each of those parenthesis, we have a perfect binomial square. That was the point of "completing the square." The x terms' perfect binomial square is\[(x-2)^{2}\]. The 2 comes from the number we had to square to get the 4 we added in. The y terms' perfect binomial square is\[(y+3)^{2}\]because the number we squared to get the 9 we added in was 3. So our equation is complete and looks like this:

Answer 11

\[(x-2)^{2}+(y+3)^{2}=25\]

Answer 12

This is a circle with center (2, -3) and radius 5.

Answer 13

ohhh that makes since now that you explained it to me thanks a bunch!!! :D

Answer 14

You're welcome! TY for the medal!

Answer 15

no problem :)