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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 300 (page 1158)

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

Short Answer

Expert verified

The graph of hyperbola is

Step by step solution

01

Step 1. Given Information

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

02

Step 2. Explanation

We will write the equation in standard form as follows,

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

As $x^{2}$ term is positive, the transverse axis is horizontal and the vertices are as follows,

$a^{2} = 4 a = 卤 \sqrt{4} a = 卤 2$

Since, $a = 卤 2$ , the vertices on x-axis are $(- 2, 0) a n d (2, 0)$ and $b = 卤 4$ , the rectangle will intersect y-axis at $(0, - 4) a n d (0, 4)$

03

Step 3. Calculation and Graph

We will find the equation of asymptote as follows,

$y = \frac{b}{a} x y = \frac{4}{2} x y = 2 x a n d y = - \frac{b}{a} x y = - \frac{4}{2} x y = - 2 x$

Sketch the asymptote through the diagonal and the vertices on the graph.

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Most popular questions from this chapter

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