00:01
For this problem, we are asked to find the center, foci, vertices, and ex -intricity of the ellipse given by the equation 3x squared plus 7y squared equals 63.
00:09
So the first thing that we want to do here is get this into the standard form of the equation of ellipse, of any ellipse, by dividing both sides by 63.
00:19
So we'll have that that turns into x squared over 21 plus y squared over 9 equals 1.
00:28
So first we can note that we clearly will have center 0 .0.
00:35
Then we can see that we'd have major axis a equals the square root of 21, minor axis b equaling the square root of 9 or positive 3.
00:47
So that means then that we will have a horizontal major axis.
00:53
In that case, we'll find that the foci will be found at 0 plus or minus c, where we have that c squared is going to equal a squared minus b squared, so that's going to be 21 minus 9, which is going to be c squared equals 12...