Chapter 9, Problem 8CT

To determine

To graph the hyperbola - $x^2-y^2+4=0$

Answer to Problem 8CT

The graph is

  

Explanation of Solution

Given:

Equation of Hyperbola: $x^2-y^2+4=0$

Formula Used:

The standard equation for hyperbola- $\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$

Asymptotes is given as: $y=\frac{a}{b}x$ and $y=-\frac{a}{b}x$

Calculation:

Given:

Equation of Hyperbola: $x^2-y^2+4=0$

  $x^2-y^2=-4$

Dividing the above equation by $-4$ on both the sides, we have:

  $\begin{array}{l}\frac{x^2-y^2}{-4}=\frac{-4}{-4}\\ \frac{x^2}{-4}+\frac{y^2}{4}=1\\ \frac{y^2}{4}-\frac{x^2}{4}=1\end{array}$

Asymptotes −

  $y=\frac{a}{b}x$

  $\begin{array}{l}y=\frac{2}{2}x\\ y=x\end{array}$

And $y=-\frac{a}{b}x$

  $\begin{array}{l}y=-\frac{2}{2}x\\ y=-x\end{array}$

Plotting hyperbola on the graph using the above details, we have:

  

Conclusion:

The graph is −