Chapter 9, Problem 49SGR

To determine

To find: The graph of the given hyperbola.

Answer to Problem 49SGR

The graph of the given hyperbola is shown in Figure-1

Explanation of Solution

Given information:

The hyperbola is $4x^2-9y^2=36$

Calculation:

Consider the equation.

  $\begin{array}{l}4x^2-9y^2=36\\ \frac{x^2}{9}-\frac{y^2}{4}=1\end{array}$

The standard equation of the hyperbola is,

  $\frac{{\left(y-k\right)}^2}{a^2}+\frac{{\left(x-h\right)}^2}{b^2}=1$

Compare above equations.

  $\left(h,k\right)=\left(0,0\right)$

Therefore, co-ordinates of verticals of the given hyperbola are

  $\begin{array}{c}\left(h\pm a,k\right)=\left(0\pm 3,0\right)\\ =\left(3,0\right)and\left(-3,0\right)\end{array}$

The graph is shown below.

  

Figure-1