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Current time:0:00Total duration:2:21

Vertices & direction of a hyperbola (example 2)

Video transcript

so we're asked to choose the equation that can represent the hyperbola graphed below and so this is the hyperbola graphed in blue and I encourage you to pause the video and figure out which of these equations are represented by the graph here all right so let's think about it this graph opens to the left and the right well I guess the first thing we can realize it's centered at zero so it's definitely it's just going to have the form x squared + y squared over two different things equaling 1 and we know that it opens to the left and the right you could think of it it opens along the x direction and so we know that the X term is going to be positive here which tells us that the Y term is going to be negative and we know that the vertices here are five to the right of the center and five to the left of the center and so since the distance from the vertices to the center is five in the horizontal direction we know that this right over here is going to be five squared or 25 25 and this we don't quite know just yet I'll just call this I'll just call this a squared a squared we don't know what a is now let's look at these choices here x squared over 25 - y squared over 9 equals 1 well that seems to match the pattern that I was able to generate really quickly just looking at the graph so I like this one this one has the X term being negative so this graph over here this would open up up and down not to the left and the right so we can we can rule this out this one over here this has x squared over 9 that would imply that our x-intercepts are our plus or minus 3 to the right and left of the center not 5 and clearly they aren't plus or minus 3 so we could rule this one out this one has the y term being positive in the X term being negative so once again this would open up and down so we could rule that one out as well and so our first choice that we liked that matched our pattern we can feel pretty good about it now if you wanted to verify the 9 or if you want you might want to try out some other points or solve some points if it wasn't multiple choice but in this case we are able to pick out the this is the only one that even matches the the general structure that we were able to deduce