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In this episode of Engineer In Training Exam TV will reinforce your understanding of the Hyperbola. We will begin by defining the general equation for a Hyperbola and then run through a few example problems.

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Jill says

Justin, Thank you for your awesome videos. I just reviewed hyperbolas. I’m confused as to why in a left to right opening hyperbola equation, k is -1, rather than 1. It seems critical to get this sign right, but there was no discussion in your idea about why in (y-k) k was assigned the value of -1, making (y-k) (y-(-1)) or (y+ k)

Erik R Hendrickson says

As above, love your videos too!

I think there’s a little mistake in the general equations:

When the transverse axis is horizontal (in other words, when the center, foci, and vertices line up side by side, parallel to the x-axis), then the a^2 goes with the x part of the hyperbola’s equation, and the y part is subtracted.

When the transverse axis is vertical (in other words, when the center, foci, and vertices line up above and below each other, parallel to the y-axis), then the a^2 goes with the y part of the hyperbola’s equation, and the x part is subtracted.

Erik R Hendrickson says

Also looks like the slopes are different between L/R and U/D hyperbolas according to other math websites…

L/R slope = b/a

U/D slope = a/b

Just trying to get it right.