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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. 165E (page 1134)

In the following exercises, graph.
$\frac{{(y - 4)}^{2}}{16} - \frac{{(x + 1)}^{2}}{25} = 1$

Short Answer

Expert verified

The graph is as below

Step by step solution

01

Step 1. Given information

The equation is $\frac{{(y - 4)}^{2}}{16} - \frac{{(x + 1)}^{2}}{25} = 1$

Draw the graph.

02

Step 2. Calculation

The y² term is positive, the transverse axis is vertical.

The hyperbola opens up and down.

Find the centre

Compare the equation with standard form $\frac{{(y - k)}^{2}}{a^{2}} - \frac{{(x - h)}^{2}}{b^{2}} = 1$

So, $(h, k) = (- 1, 4)$ and $a^{2} = 16 鈬� a = 卤 4$

$b^{2} = 25 鈬� b = 卤 5$

Sketch the rectangle that goes through the points 4 units above/below the centre

5 units left/right of centre

03

Step 3. Draw the graph

Sketch the graph using asymptotes.

The graph is

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