hyperbola

(noun)

a conic section formed by the intersection of a cone with a plane that intersects the base of the cone and is not tangent to the cone

Related Terms

Examples of hyperbola in the following topics:

  • Conic Sections in Polar Coordinates

    • Traditionally, the three types of conic section are the hyperbola, the parabola, and the ellipse.
    • The type of a conic corresponds to its eccentricity, those with eccentricity less than 1 being ellipses, those with eccentricity equal to 1 being parabolas, and those with eccentricity greater than 1 being hyperbolas.
    • As in the figure, for $e = 0$, we have a circle, for $0 < e < 1$ we obtain an ellipse, for $e = 1$ a parabola, and for $e > 1$ a hyperbola.

  • Conic Sections

    • Traditionally, the three types of conic section are the hyperbola, the parabola, and the ellipse.
    • The type of a conic corresponds to its eccentricity—those with eccentricity less than 1 being ellipses, those with eccentricity equal to 1 being parabolas, and those with eccentricity greater than 1 being hyperbolas.
    • If they are bound together, they will both trace out ellipses; if they are moving apart, they will both follow parabolas or hyperbolas.
    • Hyperbola.

  • Hyperbolic Functions

    • Just as the points ($\cos t$, $\sin t$) form a circle with a unit radius, the points ($\cosh t$, $\sinh t$) form the right half of the equilateral hyperbola.