Chapter 9.5, Problem 9OE

To determine

To graph: the equation with proper description.

Answer to Problem 9OE

The variable $x$ which is positive therefore the graph is horizontal hyperbola.

Explanation of Solution

Given:

  $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1.$

Concept used:

The equation of hyper bola:

  $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1.$

Major axis= $2a$ .

Minor axis= $2b$ .

From the given equation it is clearly point out that the geometry is hyperbola and its horizontal due to the variable $x$ which is positive.

Semi major axis is $a$ .

Semi minor axis is $b$ .

Calculation:

According to the given:

  $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1.$

From the given equation it is clearly point out that the geometry is hyperbola and its horizontal due to the variable $x$ which is positive.

The graph so form will depend on the value of $a\text{ and }b$ the semi major axis of the hyperbola.

Let the semi major axis be $a=2$ .

Similarly, semi minor axis be $b=-2$ .

The graph can be plot using the equation of hyperbola:

  $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1.$

The graph of such function can be drawn as:

  

Hence, the variable $x$ which is positive therefore the graph is horizontal hyperbola.