Question

How do you know if a hyperbola is open?

Answer 1

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 the$x$ term is positive.

$${\displaystyle \frac{{(x-h)}^2}{a^2}}-{\displaystyle \frac{{(y-k)}^2}{b^2}}=1$$
That means the curves open left and right.
It is a vertical hyperbola if the$y$ term is positive.

$\frac{{(y-k)}^2}{a^2}-\frac{{(x-h)}^2}{b^2}=1$

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.