Because we're going to do number 11 right now.
So we have your attention--
No?
I've never really thought of that.
No.
All right, ladies and gentlemen, I just
want to make sure I go through this to make sure we're always
at least on the same page before I
go to the other types of problems we have.
So first of all, again, just like parabolas,
we need to determine-- there's two types of ellipses
we can have.
We could have one ellipse where we have a major axis
of symmetry like here your x-axis is going to be--
the mayor axis means the longer part
is going to be your major axis symmetry-- or we could have it
where we're going a vertical axis of symmetry.
And of course, just like parabolas, these
have two different equations.
All right?
For ellipses, the way that we're going
to be able to determine this is we're
going to look at our major axis of symmetry has a length of 2a.
So it doesn't matter where it is, if it's vertical
or if it's horizontal, the distance of it is 2a.
All right?
And our major axis
[GASP] What?
You're in this now?
Oh.
So our major axis is going to be always under whatever term
we have.
If you look at this, the term-- or minor axis
is what we call this-- is going 2b.
And you can honestly see that b is smaller than a, right?
Yes.
OK.
So how we're going to look at this
is if I notice what we have is our general form,
we either have a squared or b squared.
And I'll write out the formula here in a second.
But whichever one is larger is going to be your x squared.
So I can say that this is going to be my a squared.
Since my a squared is under my y-coordinate,
I know that this is going to be a vertical axis of symmetry.
Just think of the y-coordinate, that's
going to be like you're on your y-axis.
So therefore, the larger point is
going to be stretched along that y-axis.
So let's just write it out.
So now that I know I have a vertical horizontal axis
symmetry, let's just write out the formula
x minus h squared all over b squared plus y minus k squared
all over a squared.
Wait, so if the a squared is under the y,
then it's got a horizontal axis?
It's vertical.
You just said that.
If it's under the y, it's a vertical
if your a, your larger number one is under the x,
then it's going to be a horizontal.
Can you write that down?
It'll be stretched horizontally.
All right?
Does anybody have any question on how to determine that?
You're gong to have to be able to determine that just
like the parabolas.
Parabolas, it's a little bit easier
because you remember oh x squared, that's vertical,
right?
Or y squared, that's going to be horizontal.
Here, you just need to determine what
is my larger number because a is always larger than b right?
Your a is always larger than your b.
Since my a is larger than my b, whatever my a is under,
that's going to determine if it's vertical or horizontal.
So they want us to determine our vertices or--
I'm sorry-- first, our center.
Well, in this problem guys, remember,
center is going to be the exact same
as our vertex in a parabola.
So center is going to be h, k.
In this problem, we have negative 3, 5.
All right?
So I'll graph something over here, so 1, 2, 3, 1, 2, 3, 4,
5.
All right?
Now, the next thing is we need to determine
what our vertices are.
Well, our vertices take a distance on.
The main important thing that you
need to understand why we have that major axis
is because your vertices, your vertex and your foci
all lie on your major axis of symmetry.
So we determine that this is going
to have a vertical major axis of symmetry.
And then, what I need to do is if here is my center,
I'm going to have a vertical axis of symmetry.
So now, what I need to do is determine if here is my center,
my two vertices-- right, we're not dealing with the horizontal
so let's just erase this.
Now if here's my vertex, my two vertices
are going to be a distance of a, a up and a down.
So I need to determine now what is the value of a.
Well, we have 25 equals a squared.
So therefore, a equals 5.
Correct?
So if I say, all right, well here's
my center at negative 3, 5, and my vertices
have to be a distance up and a distance down.
It makes sense?
Yes.
So the first vertice is another 5 up.
So if I'm at negative 3, 5, 6, 7, 8, 9, 10.
And then down 5, which would be at 0.
So my vertices are gong to be at--
they're still gong to be negative 3.
The h-coordinate cannot change, but now I'm going to negative
3, 10 and negative 3, 0 plus or minus 5.
I found the value of a, which is five
and I added it and I subtracted it.
So here's my center.
Here's my vertice and there's my vertice.
I know my graph's not perfect, but what it's OK.
We cool on that now?
Wait, you did what?
Did what?
Oh, I see.
Never-mind.
The next thing we need to take a look at
is now we need to figure out our foci.
You're looking at me like I'm stupid.
No, I'm not looking at you like you're stupid at all,
but I gave you that look because you're staring.
I just--
I'm spacing out.
There's only one person talking.
And it doesn't help when you keep on turning around, too.
I need to help me stay awake.
OK, [? but Ara ?] you've covered this so far [INAUDIBLE].
Yes.
I just found the center and I took the vertices, right?
Yeah.
And then we figured out what a is
and then I'm adding and subtracting that to there.
So the next thing I want to do is
we need to figure out the foci is.
Well, ladies and gentlemen, we have an issue with the foci
because the foci, the distance of their foci is c.
And the problem with c is we know that here our minor axis
is 2b, our major axis is 2a.
But we don't know the value of the c.
Luckily, we do have a relationship
to find the value of c which is a squared minus b squared.
All right?
So we can figure out what the value of c
is as long as you know what a squared and b squared are.
So I have c squared equals a squared which is
25 minus b squared which is 16.
c squared equals 9.
c equals 9.
c equals 3, right?
So now, our foci is going to be the exact same thing.
Notice how our center, our foci and our vertices
all lie on the same major axis.
So now, if I know that this distance is 3, all I need to do
is add 3 and subtract 3 to the y-coordinate of your center.
So my foci is still going to be negative 3.
I'm not moving left or right at all,
but now it's going to be negative 3,
5 plus 3, which is 8, negative 3, 5 minus 3 which is two.
All right?
And so there is 3.
There's my foci.
Here's my foci.
And I'm not going to graph the minor axis.
My minor axis would have been 2b.
So that would have been 16.
So we would have had 2 over 2.
So it would have actually been right there like that.
That's a graph with the minor axis to go through.
But I'm just giving you guys a rough sketch.
The main important thing is remembering these are all
on your major axis.
OK?
OK.
Yeah, it doesn't scare me.
I can barely keep my eyes open.