# Hyperbolas at the Origin - Video Tutorials & Practice Problems

## Introduction to Hyperbolas

Given the hyperbola $\frac{{x}^{2}}{25}-\frac{{y}^{2}}{9}=1$, find the length of the $a$-axis and the $b$-axis.

$a=25,b=9$

$a=9,b=25$

$a=5,b=3$

$a=3,b=5$

Given the hyperbola ${x}^{2}-\frac{{y}^{2}}{4}=1$, find the length of the $a$-axis and $b$-axis.

$a=1,b=4$

$a=4,b=1$

$a=1,b=2$

$a=2,b=1$

Given the hyperbola $\frac{{y}^{2}}{100}-\frac{{x}^{2}}{139}=1$, find the length of the $a$-axis and the $b$-axis.

$a=100,b=139$

$a=139,b=100$

$a=\sqrt{139},b=10$

$a=10,b=\sqrt{139}$

## Foci and Vertices of Hyperbolas

Determine the vertices and foci of the hyperbola $\frac{y^2}{4}-x^2=1$.

Vertices: $\left(2,0\right),\left(-2,0\right)$

Foci: $\left(\sqrt5,0\right),\left(-\sqrt5,0\right)$

Vertices: $\left(0,2\right),\left(0,-2\right)$

Foci: $\left(0,\sqrt5\right),\left(0,-\sqrt5\right)$

Vertices: $\left(1,0\right),\left(-1,0\right)$

Foci: $\left(5,0\right),\left(-5,0\right)$

Vertices: $\left(0,1\right),\left(0,-1\right)$

Foci: $\left(0,5\right),\left(0,-5\right)$

Find the equation for a hyperbola with a center at $(0,0)$, focus at $(0,-6)$ and vertex at $(0,4)$ .

$\frac{{y}^{2}}{16}-\frac{{x}^{2}}{20}=1$

$\frac{{y}^{2}}{20}-\frac{{x}^{2}}{16}=1$

$\frac{{y}^{2}}{4}-\frac{{x}^{2}}{\sqrt{20}}=1$

$\frac{{y}^{2}}{\sqrt{20}}-\frac{{x}^{2}}{4}=1$

## Asymptotes of Hyperbolas

Find the equations for the asymptotes of the hyperbola $\frac{{x}^{2}}{64}-\frac{{y}^{2}}{100}=1$.

$y=\pm \frac{4}{5}x$

$y=\pm \frac{5}{4}x$

$y=\pm \frac{16}{25}x$

$y=\pm \frac{25}{16}x$

Find the equations for the asymptotes of the hyperbola $\frac{{y}^{2}}{16}-\frac{{x}^{2}}{9}=1$.

$y=\pm \frac{9}{16}x$

$y=\pm \frac{16}{9}x$

$y=\pm \frac{3}{4}x$

$y=\pm \frac{4}{3}x$

## Graph Hyperbolas at the Origin

## Graphing Hyperbolas at the Origin Example 1

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