00:01
So the first thing we're being asked to do is to rewrite the given equation of a circle in standard form.
00:05
So remember, in standard form, that would look like this.
00:07
X minus h quantity squared plus y minus k quantity squared equals r squared, where our center is located at the point, hk, and r is our radius.
00:19
So in order to do this, what we need to do is use a process called completing the square.
00:24
So first, we're going to focus on our x terms.
00:26
So we need to find the value to add to x squared plus 10x that will make it a perfect.
00:30
Square.
00:31
So to do this, we're going to use b divided by 2 squared, where b is the coefficient of our x term, which in this case is 10.
00:38
So we'll do 10 divided by 2 quantity squared.
00:41
Well, 10 divided by 2 is 5, and 5 squared is 25.
00:44
So we're going to rewrite this as x squared plus 10x plus 25.
00:49
But if we add 25 to the left -hand side of our equation, we also have to add it to the right -hand side.
00:55
Now, we're going to do the same process with our y terms.
00:58
So our b value in this case is negative 4, so we're going to have negative 4 divided by 2 squared.
01:03
Well, negative 4 divided by 2 is negative 2, and negative 2 squared is positive 4.
01:07
So this will leave us with y squared minus 4 y plus 4.
01:12
But if we add 4 to the left -hand side, we'll also have to add 4 to the right -hand side.
01:17
Now, with that constant of 13 there, what we need to do is move it to the right -hand side of our equation.
01:22
So to do this, we'll subtract 13 from both sides.
01:26
Okay, so now let's see what we'll left with.
01:28
Well, first we have x squared plus 10x plus 25.
01:31
Remember, we use completing the square, so that way we would make it a perfect trinomial...