Ellipses and Hyperbolas

Hyperbola Standard Form

Write the standard equation of a centered horizontal hyperbola and identify its center and vertices.

Example

Use a and b to write and plot a centered hyperbola.

highlighted = computed this step

Step 1 — Read a and b

Read a and b for the hyperbola.

a=3b=4a= \hl{3} \quad b= \hl{4}

Step 2 — Square the axes

Square a and b for the denominators.

a2=9b2=16a^{2} = \hl{9} \quad b^{2} = \hl{16}

Step 3 — Standard form

Write the centered hyperbola standard form.

x29−y216=1\frac{x^{2}}{ \hl{9} } - \frac{y^{2}}{ \hl{16} } = 1

Step 4 — Plot the hyperbola

Plot the hyperbola and vertices.

Coordinate plot\text{Coordinate plot}
Hyperbola standard form plotCentered horizontal hyperbola with left and right vertices.LR

Step 5 — Vertices

State the left and right vertices.

L=(-3,0)R=(3,0)L=( \hl{-3} , \hl{0} ) \quad R=( \hl{3} , \hl{0} )
hyperbola-standard-form For a centered horizontal hyperbola, x^2/a^2 - y^2/b^2 = 1. The vertices are a units left and right of the center.