00:01
So let's find the equation of another hyperbola.
00:03
I'm going to give you some information.
00:04
So we know this is a hyperbola, and we know there are going to be two forms for a hyperbola, whether it opens left, right, or up, down.
00:11
So i can't write the standard form yet.
00:14
And let's say i tell you that it is centered at the point 5 .3.
00:19
So again, that's still not enough information to know whether it's going to open left, right, or up down.
00:25
And let's say further, i tell you that it has a vertex at the point 5.
00:31
Six, and it goes through the point one and eight.
00:39
So now if i do just a quick little sketch of my hyperbola here, i know that we'll go one, two, three, four, five, and one, two, well, let's stick another point in there, three.
00:55
So there is my center.
00:58
I know a vertex is at the point five, six, so five, and i'd go up three more units.
01:05
And there is a verticy.
01:07
Okay, i know which way this is going to open.
01:10
Because i know that the transverse axis is going to end up being vertical.
01:15
So i know that the equation for my hyperbole, just my general equation is going to have the y term first.
01:22
So, y minus k squared over a squared minus x minus h over b squared equals 1.
01:36
So i know that that's my standard form.
01:39
Usually make more mistakes on hyperboise that are oriented with the y squared term.
01:45
And so just make sure you put the h with the x and the k with the y.
01:51
So i actually know enough information now to fill this in and this because i know the center and the center this is the h and this is the k.
02:01
I know that five will stand for my h and i know k will stand for my three.
02:06
And i also know another little piece of information here.
02:09
I know that this distance from the center to the vertex is my a, and i can just count the squares, and i can see that a is three.
02:21
So now let's see what else i gave you.
02:23
I gave you, so, well, and by the way, there would be another vertex.
02:27
Let me go back to black.
02:29
If i moved up three units from the center, if i moved down three units from the center, there would actually be another vertex here at the point five zero.
02:37
And i know that my hyperbola would open upward.
02:41
Now how sharply it turns upward and downward, i don't know...