Chapter 11: Q. 304 (page 1158)

In the following exercises, graph.
$\frac{{(y - 1)}^{2}}{25} - \frac{{(x - 2)}^{2}}{9} = 1$

Short Answer

Expert verified

The graph of hyperbola is

Step by step solution

Step 1. Given Information

The given equation is $\frac{{(y - 1)}^{2}}{25} - \frac{{(x - 2)}^{2}}{9} = 1$

Step 2. Explanation

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

Thus,

$a^{2} = 25 a = \sqrt{25} a = 5 A n d b^{2} = 9 b = \sqrt{9} b = 3$

Thus, center is $(2, 1)$ and $a = 5, b = 3$

Step 3. Calculation and Graph

We will find the equation of asymptote as follows,

$y = \frac{a}{b} (x - h) + k y = \frac{5}{3} (x - 2) + 1 y = \frac{5}{3} x - \frac{10}{3} + 1 y = \frac{5}{3} x - \frac{7}{3} A n d y = - \frac{5}{3} (x - 2) + 1 y = - \frac{5}{3} x + \frac{10}{3} + 1 y = - \frac{5}{3} x + \frac{13}{3}$

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

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In the following exercises, graph.
$\frac{{(y - 1)}^{2}}{25} - \frac{{(x - 2)}^{2}}{9} = 1$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

Step 3. Calculation and Graph

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In the following exercises, graph.(y-1)225-(x-2)29=1

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

Step 3. Calculation and 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.
$\frac{{(y - 1)}^{2}}{25} - \frac{{(x - 2)}^{2}}{9} = 1$