Chapter 11: Q. 158E (page 1134)

In the following exercises, graph.
$9 x^{2} - 4 y^{2} = 36$

Short Answer

Expert verified

The graph is below

Step by step solution

Step 1. Given information

The equation is $9 x^{2} - 4 y^{2} = 36$ .

Draw the graph.

Step 2. Calculation

Divide the equation by 36.

$\frac{9 x^{2}}{36} - \frac{4 y^{2}}{36} = \frac{36}{36} \frac{x^{2}}{4} - \frac{y^{2}}{9} = 1$

The x² term is positive, the transverse axis is horizontal.

Here, $a^{2} = 4 \Rightarrow a = \pm 2$

So, the vertices on x- axis are $(2, 0), (- 2, 0)$ .

Now, $b^{2} = 9 \Rightarrow b = \pm 3$

The vertices on y- axis are $(0, 3), (0, - 3)$ .

So asymptote have the equations,

$y = \frac{3}{2} x$

$y = - \frac{3}{2} x$

Step 3. Draw the graph

Draw the graph using asymptotes.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the following exercises, graph.
$9 x^{2} - 4 y^{2} = 36$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

Step 3. Draw the graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Discrete Mathematics

Logic and Functions

Decision Maths

Pure Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, graph.9x2-4y2=36

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

Step 3. Draw the graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Discrete Mathematics

Logic and Functions

Decision Maths

Pure Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, graph.
$9 x^{2} - 4 y^{2} = 36$