00:01
We want to write the equation of the ellipse with fosi at negative 25 and 6 .5.
00:17
And then we have vertices at negative 35 and 7 .5.
00:40
All right.
00:43
Well our first off our equation will have the form x minus h squared over a squared plus y minus k squared over b squared equals 1 our center is hk now the center is halfway between the foci and it's also halfway between the vertices so we're finding the midpoint of the foci and we're also finding the midpoint of the vertices either way we should get the same point for the center.
01:30
So i'm going to start by finding the midpoint of the fosite.
01:33
You would have negative 2 plus 6 divided by 2 for the x coordinate, and then the y coordinate you would have 5 plus 5 divided by 2.
01:48
And that point will be negative 2 plus 6 is 4, 4 divided by 2 is 2, 5 plus 5 is 10, and 10 divided by 2 is 5.
01:59
So our center is at 2 .5.
02:01
Now i'm going to double check that with the vertices.
02:04
Negative 3 plus 7 is 4, and 4 divided by 2 is 2.
02:08
That's coordinates 2, and then your y coordinate has to be 5 because you know that the y coordinate of the vertices will be the same as the y coordinate of the foci and the same as the y coordinate of the center.
02:22
So here's our equation.
02:25
We'll have x minus 2 squared over a squared plus, now y minus k will be y minus 5 squared over b squared and that equals 1.
02:57
Now we've got to find the a squared and the b squared.
03:01
And we know that the distance from the center to the end point of the major axis will be our a squared.
03:17
Or it'll be the b squared.
03:19
Let's look at our foci at our center.
03:22
Negative 2, 5, 2, 3, 4, 5.
03:30
That's a fosite...