Chapter 11: Q. 303 (page 1158)

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

Short Answer

Expert verified

The graph of hyperbola is

Step by step solution

Step 1. Given Information

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

Step 2. Explanation

As $y^{2}$ term is positive, the transverse axis is vertical. On comparing with the standard form, we get, $(h, k) = (- 1, - 2)$ .

Thus,

$a^{2} = 9 a = \sqrt{9} a = 3 A n d b^{2} = 9 b = \sqrt{9} b = 3$

Thus, center is $(- 1, - 2)$ and $a = 3, b = 3$

Step 3. Calculation and Graph

We will find the equation of asymptote as follows,

$y = \frac{a}{b} (x - h) + k y = \frac{3}{3} (x + 1) - 2 y = x + 1 - 2 y = x - 1 A n d y = - \frac{a}{b} (x - h) + k y = - \frac{3}{3} (x + 1) - 2 y = - x - 1 - 2 y = - x - 3$

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

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

Step 3. Calculation and Graph

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Step by step solution

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Step 2. Explanation

Step 3. Calculation and Graph

One App. One Place for Learning.

Most popular questions from this chapter

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In the following exercises, graph.
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