Chapter 9, Problem 50SGR

To determine

To find: The graph of the given hyperbola.

Answer to Problem 50SGR

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

Explanation of Solution

Given information:

The hyperbola is $9y^2-x^2-4x+18y+4=0$

Calculation:

Consider the equation.

  $\begin{array}{l}9y^2-x^2-4x+18y+4=0\\ \frac{{\left(y+1\right)}^2}{\frac{1}{9}}-\frac{{\left(x+2\right)}^2}{1}=1\end{array}$

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.

  $\left(h,k\right)=\left(-2,-1\right)$

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

  $\begin{array}{c}\left(h\pm a,k\right)=\left(-2,-1\pm \frac{1}{3}\right)\\ =\left(-2,-\frac{2}{3}\right)and\left(-2,-\frac{4}{3}\right)\end{array}$

The graph is shown below.

  

Figure-1