Chapter 11: Q. 168E (page 1069)

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

Short Answer

Expert verified

The graph is

Step by step solution

Step 1. Given information

The equation is $\frac{{(x + 2)}^{2}}{4} - \frac{{(y - 1)}^{2}}{9} = 1$ .

Step 2. Calculation.

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

The hyperbola opens left and right.

Find the centre from the equation.

Compare the equation with the standard form.

$\frac{{(x - h)}^{2}}{a^{2}} - \frac{{(y - k)}^{2}}{b^{2}} = 1$

So, $(h, k) = (- 2, 1)$ and $a^{2} = 4 \Rightarrow a = \pm 2$ and localid="1645724144236" $b^{2} = 9 \Rightarrow b = \pm 3$

Sketch the rectangle that goes through the points 2 unit left/right of the centre 3 units above/ below the centre.

Step 3. Draw the graph.

Sketch the asymptotes and draw the graph

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

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation.

Step 3. Draw the graph.

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In the following exercises, graphx+224-y-129=1

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

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Study anywhere. Anytime. Across all devices.

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