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Question

How do you know if a hyperbola is open?


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Solution

Difference between hyperbola open up and down And open left and right :

First, we check if it is a horizontal or vertical hyperbola.

It is a horizontal hyperbola if thex term is positive.

(xh)2a2(yk)2b2=1
That means the curves open left and right.
It is a vertical hyperbola if they term is positive.

(yk)2a2(xh)2b2=1

That means the curves open up and down.
So, If the y term of a hyperbola is known to have a minus sign, then the hyperbola is said to open left and right.

On the other hand, if the x term of the hyperbola has the minus sign, then the hyperbola is known to open up and down.


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