Q. 31 In Problems 29鈥�36, find the ce... [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. 31 (page 668)

In Problems 29鈥�36, find the center, transverse axis, vertices, foci, and asymptotes. Graph each equation by hand. Verify your graph using a graphing utility. $4 x^{2} - y^{2} = 16$

Short Answer

Expert verified

$Center : (0, 0) Transverse axis : x - a x i s Vertices : (卤 2, 0) Foci : (卤 2 \sqrt{5}, 0) Asymptotes : y = 卤 2 x$

Graph of the equation is:

Step by step solution

Step 1. Given information

Equation of hyperbola, $4 x^{2} - y^{2} = 16$

Writing the equation in standard form,

role="math" localid="1647142549433" $\frac{4 x^{2}}{16} - \frac{y^{2}}{16} = 1 鈬� \frac{x^{2}}{4} - \frac{y^{2}}{16} = 1$

Step 2. Finding the center, transverse axis, vertices, foci, and asymptotes of hyperbola

Comparing the given equation with standard form, $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1, b^{2} = c^{2} - a^{2}$

$a = 2, b = 4, c = 卤 \sqrt{b^{2} + a^{2}} 鈬� c = 卤 \sqrt{4^{2} + 2^{2}} 鈬� c = 卤 \sqrt{16 + 4} 鈬� c = 卤 \sqrt{20} 鈬� c = 卤 2 \sqrt{5}$

role="math" localid="1647143880701" $Center : (0, 0) Transverse axis : x - a x i s Vertices : (卤 a, 0) = (卤 2, 0) Foci : (卤 c, 0) = (卤 2 \sqrt{5}, 0) Asymptotes : y = 卤 \frac{b}{a} x 鈬� y = 卤 \frac{4}{2} x 鈬� y = 卤 2 x$

Step 3. Graph of the equation

Graph of the equation is:

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91影视

In Problems 29鈥�36, find the center, transverse axis, vertices, foci, and asymptotes. Graph each equation by hand. Verify your graph using a graphing utility. $4 x^{2} - y^{2} = 16$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding the center, transverse axis, vertices, foci, and asymptotes of hyperbola

Step 3. Graph of the equation

One App. One Place for Learning.

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91影视

In Problems 29鈥�36, find the center, transverse axis, vertices, foci, and asymptotes. Graph each equation by hand. Verify your graph using a graphing utility.4x2-y2=16

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding the center, transverse axis, vertices, foci, and asymptotes of hyperbola

Step 3. Graph of the equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Logic and Functions

Geometry

Mechanics Maths

Discrete Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

In Problems 29鈥�36, find the center, transverse axis, vertices, foci, and asymptotes. Graph each equation by hand. Verify your graph using a graphing utility. $4 x^{2} - y^{2} = 16$