Chapter 11: Q. 175E (page 1134)

In the following exercises, graph each equation.
$\frac{{(y - 3)}^{2}}{9} - \frac{{(x + 2)}^{2}}{16} = 1$

Short Answer

Expert verified

The graph is

Step by step solution

Step 1. Given information

The equation is $\frac{{(y - 3)}^{2}}{9} - \frac{{(x + 2)}^{2}}{16} = 1$

Draw the graph.

Step 2. Calculation

In the equation,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, $(h, k) = (- 2, 3)$ and localid="1646033763938" $a^{2} = 9 \Rightarrow a = \pm 3$ also $b^{2} = 16 \Rightarrow b = \pm 4$

The rectangle will pass through the points 3 units above/below the centre, 4 units left/right of centre

Step 3. Draw the graph

Draw the graph using asymptotes.

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In the following exercises, graph each equation.
$\frac{{(y - 3)}^{2}}{9} - \frac{{(x + 2)}^{2}}{16} = 1$

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, graph each equation.y-329-x+2216=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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In the following exercises, graph each equation.
$\frac{{(y - 3)}^{2}}{9} - \frac{{(x + 2)}^{2}}{16} = 1$