And now, we can substitute this and this back into this equation, and we get so dy over dx, that is equal to this.

So the entire time, the contents, the sum of the distances to the two foci was equal to 2a.

So we're saying this function, when does this function equal 0?

But if you just pick a simple a is equal to 1, than what's b equal to?

What is y divided by x gonna be equal to ?

So let's say we had x squared minus 9 over 5x plus 15.

And what's the antiderivative of this?

3 s times the Laplace transform of t squared.

So we have 5 2.

2 minus 7 over 11.

Let's just distribute the e the minus st.

All right, the coefficient in front of the x squared term is equal to a 1.

So if we were to take minus 11x squared divided by 2x, that is equal to what?

Well we're going from zero to what? x is equal to 8 here.

Well, that looks just like this if our 2 was equal to our c.

And so this becomes x minus 1 squared plus y plus 2 squared is equal to 4 plus 1 plus 4 is equal to 9.

And what does that equal?

Plus 4 is 8.

All of that over 4.

And the focal length this a squared plus b square.

So this is equal to five y plus four thirds

Two times oh, something weird happened to my pen.

We saw that at the beginning of this video.

Now this is starting to look a little bit interesting.

So that equals 54 minus 126 is 24 plus 26 is 50.

You're gonna force them to leave.

And then how high is this rectangle?

Negative 7 times that x is going to be equal to negative 7 times that x.

3 45 135.

Which is the same thing as four plus four. That would also get you eight.

Well, we know that the diameter times pi, we know that pi times the diameter is equal to the circumference is equal to 10 meters.

So if I do 2x plus x plus 3x that's going to equal 120 feet.

Laplace transform of sine of at that is equal to u prime v.

Now what we want to know is what x values make this inequality true?

I'm going to write that's equal to fifty plus four.

Because 2 3 times 15.

I could have drawn four prime marks, but either way.

So if I multiply, if I distribute this out, this is equal to what?

So f of 5 equals 5 plus 3 times g of 5.

Two times four could've been written as four plus four as well.

Because in this situation, we don't know what f of 0 is.

And here the perimeter will be 1 4 2 2 we'll scroll over to the right just a little bit 4 6 .

So minus 3 times e to the minus 3x.

What is 3 plus 1?

3 times 9 is 27.