Q. 14 For the hyperbola y216-x281=1, t... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 10: Q. 14 (page 667)

For the hyperbola $\frac{y^{2}}{16} - \frac{x^{2}}{81} = 1$ , the asymptotes are _ and ___

Short Answer

Expert verified

For the hyperbola $\frac{y^{2}}{16} - \frac{x^{2}}{81} = 1$ , the asymptotes are $y = \frac{2}{3} x$ and $y = \frac{- 2}{3} x$ .

Step by step solution

Step 1. Given Information

The equation of the hyperbola is $\frac{y^{2}}{16} - \frac{x^{2}}{81} = 1$ .

Step 2. Aim of the problem

Here, we need to find the asymptotes of the hyperbola $\frac{y^{2}}{16} - \frac{x^{2}}{81} = 1$ .

Step 3. Concept

The asymptotes of a hyperbola whose equation is of the form $\frac{{(y - k)}^{2}}{a^{2}} - \frac{{(x - h)}^{2}}{b^{2}} = 1$ is $y - k = 卤 \frac{a}{b} (x - h)$ .

Step 4. Finding the asymptotes

The given equation $\frac{y^{2}}{16} - \frac{x^{2}}{81} = 1$ is of the form $\frac{{(y - k)}^{2}}{a^{2}} - \frac{{(x - h)}^{2}}{b^{2}} = 1$ , where $(h, k) = (0, 0)$ and $a^{2} = 16$ and $b^{2} = 81$ .

Since, $a^{2} = 16,$ we have, $a = \sqrt{16} = 4$ and $b = \sqrt{81} = 9$ .

Therefore, the asymptotes are:

role="math" $y - k = 卤 \frac{a}{b} (x - h) y - 0 = 卤 \frac{4}{9} (x - 0) y = 卤 \frac{2}{3} x y = \frac{2}{3} x o r y = \frac{- 2}{3} x$

Therefore, the asymptotes of the hyperbola are $y = \frac{2}{3} x$ and $y = \frac{- 2}{3} x$

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91影视

For the hyperbola $\frac{y^{2}}{16} - \frac{x^{2}}{81} = 1$ , the asymptotes are _ and ___

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Aim of the problem

Step 3. Concept

Step 4. Finding the asymptotes

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91影视

For the hyperbola y216-x281=1, the asymptotes are _____ and _______

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Aim of the problem

Step 3. Concept

Step 4. Finding the asymptotes

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Logic and Functions

Mechanics Maths

Geometry

Applied Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

For the hyperbola $\frac{y^{2}}{16} - \frac{x^{2}}{81} = 1$ , the asymptotes are _ and ___