If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## Algebra (all content)

### Course: Algebra (all content)ย >ย Unit 17

Lesson 8: Introduction to hyperbolas

# Vertices & direction of a hyperbola

Sal picks the graph of y²/9-x²/4=1 based on the hyperbola's center, direction, & vertices.

## Want to join the conversation?

• I understand that bยฒ is nine because the distance between the center and the vertex of the hyperbola is three. However, I am confused by the aยฒ amount, four. In an ellipse this would mean two was the length of the minor radius, but there is not minor radius in a hyperbola as far as I know, so what does the four mean?
• Good question. The 2 relates to the change in x on the asymptote. If you look at these graphs you can imagine diagonal lines going through the origin that the graph would get close to but never touch. These are asymptotes. The equations of the lines for the hyperbola on the left are y=3/2x and y=-3/2x. The 3 comes from the aยฒ value being 9, and the 2 comes from the bยฒ value being 4.
• i am confused the equation of a ellipse looks exactly similar to the one shown in this video ..... so how to spot the difference ?
• Similar, but not exactly the same.
The equation of an ellipse is xยฒ/aยฒ + yยฒ/bยฒ = 1
But for a hyperbola we have xยฒ/aยฒ - yยฒ/bยฒ = 1
One has a plus: the ellipse, the other has a minus: the hyperbola
• At in the upper right corner would a^2 be 9 and b^2 be 4?
• Yes, but there is no standard hyperbola form. This problem has a positive y term and a negative x term, so if you assign a to the positive term it is. Some people will always assign a to the x term.
(1 vote)
• I guess 'the vertices of hyperbola and the vertex of parabola has the opposite meaning to that of ellipse'. In ellipse the point(s) which is farthest from the center is the vertex . And the point(s) closest to the center is it's co-vertex.
But here , in case of hyperbola and parabola, why do we call the points closer to the center as vertices not co-vertices?. That's really confusing to me.
All these are conic sections but why the naming is different?
• It is because there is only one point closest as it extends to infinity there is no farthest point. If everything had vertices and co-vertices, every point on a circle would be both. So, they are conic sections only because we can cut them from a cone. But for naming schemes, they are almost independent.
(1 vote)
• Hi, I was wondering if the equation y=7/x would be a hyperbola, since all of these examples aren't diagonal.
(1 vote)
• Yes! Any function with the equation A/x (where A is a constant) is considered to be a rectangular hyperbola.
• Where do the b^2 and a^2 come from? I understand the way the equation in manipulated but not the way they show in the graph. Please help.
(1 vote)
• So based on the equation of a vertical hyperbola, would 9 = a^2 and 4 = b^2?

"2a" is the major axis?
"2b" is the minor axis?

Where is the major and minor axis on a hyperbola graph?
(1 vote)
• What if option C had also it's center at 3, how can I figure out which one is correct? choosing a point and see if its correct?
(1 vote)
• Yeah, choosing a point and checking which is closer to the graph I think is the simplest way of doing it. You may have to use approximations though.
(1 vote)
• Why do you set the x term to equal 0?
(1 vote)
• Its so you can solve for y which give you the vertices, sorry for the really late response lol
(1 vote)
• sal khan's voice is so hot...