# Hyperbola - Other Definitions, Features, Drawing Hyperbolas, Uses

###
plane intersection nappes curve

A hyperbola is a **curve** formed by the intersection of a right circular cone and a **plane** (see Figure 1). When the plane cuts both nappes of the cone, the intersection is a hyperbola. Because the plane is cutting two nappes, the curve it forms has two U-shaped branches opening in opposite directions.

## Additional Topics

A hyperbola can be defined in several other ways, all of them mathematically equivalent:
Figure 1. Illustration by Hans & Cassidy. Courtesy of Gale Group.
Figure 2. Illustration by Hans & Cassidy. Courtesy of Gale Group.
Figure 3. Illustration by Hans & Cassidy. Courtesy of Gale Group.
…

A hyperbola is symmetric about both its transverse and its conjugate axes.
…

Hyperbolas can be sketched quite accurately by first locating the vertices, the foci, and the asymptotes. Starting with the axes, locate the vertices and foci. Draw a circle with its center at C, passing through the two foci. Draw lines through the vertices perpendicular to the transverse axis. This determines four points, which are corners of a rectangle. These diagonals are the asymptotes. Using…

Hyperbolas have many uses, both mathematical and practical. The hyperbola y = 1/x is sometimes used in the definition of the natural logarithm. In Figure 6 the logarithm of a number n is represented by the shaded area, that is, by the area bounded by the x-axis, the line x = 1, the line x = n, and the hyperbola. Of course one needs calculus to compute this area, but there are techniques for doing …

## Citing this material

Please include a link to this page if you have found this material useful for research or writing a related article. Content on this website is from high-quality, licensed material originally published in print form. You can always be sure you're reading unbiased, factual, and accurate information.

Highlight the text below, right-click, and select “copy”. Paste the link into your website, email, or any other HTML document.

## User Comments