00:01
So for the very first question, we're looking for vertices and the focal points from the hyperbola.
00:05
The fact that x squared is first tells us that we have ourselves a horizontal hyperbola.
00:11
So it's going to look like this.
00:12
Now, the center appears to be at zero -zero, since there's nothing with x squared and y -squared.
00:18
So underneath here, always the first is always a -squared.
00:21
Underneath, the second one is always b -squared.
00:23
That doesn't flip.
00:24
So if this is a -squared, that tells me the value of a is going to be equal to seven.
00:28
And the value of b is going to be equal to 2.
00:31
Well, the distance from the center to the vertex of each of these pieces here is a.
00:37
So that means that the vertices are going to have to be at negative 7, 0, and 7 .0.
00:45
So now i need to define c to find the focal points.
00:48
So right now i can knock out answer choices c and d.
00:51
So to find c, i'm going to do pythagorean theorem.
00:53
So 49 plus 4 is equal to c squared.
00:56
4 -9 plus 4 is 53.
00:59
So 53 is c squared, so the square root of 53 is equal to c or plus or minus.
01:04
So the focal points here are the distance of c.
01:08
So we would have negative square root of 53 comma 0, and then positive square root of 53 comma 0.
01:15
So it looks like we are looking at answer choice b for this one.
01:19
So for the second one, it looks like we're trying to match the equation with the graphs...