Chapter 11: Q. 157E (page 1134)

In the following exercises, graph
$4 x^{2} - 16 y^{2} = 64$

Short Answer

Expert verified

The graph is as follows

Step by step solution

Step 1. Given information

The equation is $4 x^{2} - 16 y^{2} = 64$

Draw the graph

Step 2. Calculation

Divide the equation by 64 and simplify

$\frac{4 x^{2}}{64} - \frac{16 y^{2}}{64} = \frac{64}{64} \frac{x^{2}}{16} - \frac{y^{2}}{4} = 1$

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

Here, $a^{2} = 16 \Rightarrow a = \pm 4$

So, the vertices on x- axis are $(4, 0), (- 4, 0)$

Now, $b^{2} = 4 \Rightarrow b \pm 2$

The vertices on y- axis are $(0, 2), (0, - 2)$

So asymptote have the equations,

$y = \frac{2}{4} x = \frac{1}{2} x$ and $y = - \frac{2}{4} x = - \frac{1}{2} x$

Step 3. Draw the graph

Draw the graph using asymptotes.

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In the following exercises, graph
$4 x^{2} - 16 y^{2} = 64$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

Step 3. Draw the graph

One App. One Place for Learning.

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In the following exercises, graph4x2−16y2=64

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

Theoretical and Mathematical Physics

Applied Mathematics

Logic and Functions

Discrete Mathematics

Probability and Statistics

Geometry

Study anywhere. Anytime. Across all devices.

In the following exercises, graph
$4 x^{2} - 16 y^{2} = 64$