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Special Things About Hyperbolas

A hyperbola is a very special curve. As seen in the following pictures, a hyperbola has two distinct parts or branches.
Figure 1
Figure 2
Figure 3

Notice that a hyperbola can open in a variety of directions. However, you will be mainly be studying hyperbolas that open up and down or left and right, as in Figures 1 and 2.
Hyperbolas like the one seen in Figure 3 will not be explored until the Extensions Module.
Like an ellipse, a hyperbola has two axes of symmetry. The axis of symmetry that is parallel to the x-axis is called the horizontal axis of symmetry. The axis of symmetry that is parallel to the y-axis is called the vertical axis of symmetry. In Figures 1, 2 and 3 the axes of symmetry are drawn in grey.
Notice that only one axis of symmetry actually intersects the hyperbola.
The points where the hyperbola crosses this axis of symmetry are called the vertices of the parabola.
Also notice that in all the graph of hyperbolas, there is a pair of intersecting blue lines. These lines are the asymptotes of the hyperbola. An asymptote is a line that a curve approaches, but never touches.
You will learn more about hyperbolas in the Hyperbola Module.

A hyperbola is a very special curve. As seen in the following pictures, a hyperbola has two distinct parts or branches.
Figure 1	Figure 2	Figure 3
Notice that a hyperbola can open in a variety of directions. However, you will be mainly be studying hyperbolas that open up and down or left and right, as in Figures 1 and 2. Hyperbolas like the one seen in Figure 3 will not be explored until the Extensions Module.
Like an ellipse, a hyperbola has two axes of symmetry. The axis of symmetry that is parallel to the x-axis is called the horizontal axis of symmetry. The axis of symmetry that is parallel to the y-axis is called the vertical axis of symmetry. In Figures 1, 2 and 3 the axes of symmetry are drawn in grey.
Notice that only one axis of symmetry actually intersects the hyperbola. The points where the hyperbola crosses this axis of symmetry are called the vertices of the parabola.
Also notice that in all the graph of hyperbolas, there is a pair of intersecting blue lines. These lines are the asymptotes of the hyperbola. An asymptote is a line that a curve approaches, but never touches.
You will learn more about hyperbolas in the Hyperbola Module.