Question

How do I tell whether a hyperbola is going to open left/right

How do I tell whether a hyperbola is going to open left/right or up/down?

Answer

That's a good question. I always remember: whichever value (x or y) is negative, the hyperbola is parallel to that axis.

If you aren't sure, use the "box method" to show where possible vertices are. (Draw a dotted box around the center using the x and y radius. The vertices lie on the outside of that box.) Then you can choose a possible vertex point, test it in the equation, and see if it is true. If it does, then that is your vertex, with the other being on the opposite side. If it is wrong, test the other points to make sure that they are the correct vertex.

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