Q. 3 - Precalculus Enhanced with Graphing Utilities

Question

Graph the equation: $y^2=x^2-1$

Step-by-Step Solution

Answer

The graph of $y^2=x^2-1$is

Step 1. Give data

The given equation is

$y^2=x^2-1$

Step 2. Properties of equation

Rearrange the equation into the standard form of the equation of the hyperbola

$$\begin{gathered} y^2=x^2-1 \\ \frac{x^2}{1^2}-\frac{y^2}{1^2}=1 \\ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \end{gathered}$$

so $$\begin{gathered} a=1 \\ b=1 \\ c=\sqrt{a^2+b^2} \\ c=\sqrt{2} \end{gathered}$$

vertices are $(\pm a,0)=(\pm 1,0)$

foci are $(0,\pm c)=(0,\pm \sqrt{2})$

Step 3. Graph

Plot a hyperbola of the vertices$(\pm 1,0)$ and foci $(0,\pm \sqrt{2})$to plot the graph of  $y^2=x^2-1$