00:02
Here we have the equation of a circle, and we want to convert it into standard form, and that's going to involve a process that we do called completing the square.
00:12
And even though in this problem, there's a lot of fractions, the concept is still the same as the previous problems we've been doing, so we can just go right ahead and follow the same procedure.
00:21
Okay, so we want to add some number to complete the square on x.
00:25
So we have to figure out what to add.
00:26
So we have x squared minus two -thirds x plus what.
00:30
What will make that a perfect square trinomeroom.
00:32
And the same for y, we have y squared plus three halves y plus what to make a perfect square trinomial.
00:41
And then on the other side of the equation, we have zero.
00:44
But whatever we add to the left side of the equation, we're going to have to also add to the right side of the equation to keep it balanced.
00:50
Now let's figure out what to add.
00:52
So remember when you complete this square, what you do is you take half of this number here.
00:57
So half of negative two thirds.
00:59
That would be negative of one -third and then you square it and that would be one -ninth.
01:03
So that's what you add.
01:04
And if i add one -ninth to the left, then i add one -ninth to the right...