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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 147E (page 1134)

In the following exercises, graph.
$\frac{x^{2}}{9} - \frac{y^{2}}{4} = 1$

Short Answer

Expert verified

The graph is

Step by step solution

01

Step 1. Given information

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

Draw the graph.

02

Step 2. Calculation

The $x^{2} -$ term is positive, the transverse axis is horizontal.

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

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

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

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

So asymptote have the equations

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

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

03

Step 3. Draw the graph

The graph is

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Most popular questions from this chapter

Alice can paint a room in 6 hours. If Kristina helps her it takes them 4 hours to paint the room. How long would it take Kristina to paint the room by herself?

For the function $f (x) = 25 x^{2} - 81$ , find:
(a) the zeros of the function.

(b) the x-intercepts of the graph

of the function.
(c) the y-intercept of the graph of the

function.

In the following exercises, simplify. $3 \sqrt{75 y^{2}} + 8 y \sqrt{48} - \sqrt{300 y^{2}}$

Simplify the complex rational expression by writing it as division:

$\frac{\frac{1}{a} + \frac{1}{b}}{\frac{1}{a^{2}} - \frac{1}{b^{2}}}$

In the following exercises, multiply the rational expressions. $\frac{5 c^{2} + 9 c + 2}{c^{2} - 25} . \frac{c^{2} + 10 c + 25}{3 c^{2} - 14 c - 5}$

See all solutions

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