00:01
We have the equation 4 y squared plus 16y minus 9 x squared is equal to 20.
00:09
Let's get this into standard 4.
00:11
So we've got our ys together.
00:14
Leave a spot to complete the square and our x is together.
00:18
Again, leave a spot to, we won't need to complete the square here.
00:24
With the ys, we should factor out of 4, leaving y squared plus 4 y.
00:28
And then to fact us complete the square with the y's half of four is two squared is four but we have to add 16 to the right hand side to stay balanced so we have four times the quantity y plus two squared minus nine x squared equals 36 divide everything by 36 36 or four over 36 is one night so we have the quantity y plus two squared over nine minus x squared over 4 equals 1.
01:08
Now we're in standard form, and we're in business, we can say that the center is at 0 -2.
01:16
Our vertices, since the a value is going to be the square of 9 or 3, the b values is square to 4 or 2, and it's a y -squared minus x -words.
01:25
It's vertically aligned, so we're going to add subtract 3 to the y -coronet that becomes 0 -2 plus 3, and 0 -2 -2 minus 3.
01:34
So 0 1 and 0 negative 5 are the vertices.
01:41
The center is at 0 negative 2...