Chapter 10: Q. 36 (page 668)

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

Short Answer

Expert verified

$Center : (0, 0) Transverse axis : x - a x i s Vertices : (\pm \sqrt{2}, 0) Foci : (\pm \sqrt{6}, 0) Asymptotes : y = \pm \sqrt{2} x$

Graph of the equation is:

Step by step solution

Step 1. Given information

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

Writing the equation in standard form,

$\frac{2 x^{2}}{4} - \frac{y^{2}}{4} = 1 \Rightarrow \frac{x^{2}}{2} - \frac{y^{2}}{4} = 1$

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

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

We get,

$a = \sqrt{2}, b = 2, c = \pm \sqrt{a^{2} + b^{2}} \Rightarrow c = \pm \sqrt{2 + 2^{2}} \Rightarrow c = \pm \sqrt{2 + 4} \Rightarrow c = \pm \sqrt{6}$

role="math" localid="1647143938271" $Center : (0, 0) Transverse axis : x - a x i s Vertices : (\pm a, 0) = (\pm \sqrt{2}, 0) Foci : (\pm c, 0) = (\pm \sqrt{6}, 0) Asymptotes : y = \pm \frac{b}{a} x \Rightarrow y = \pm \frac{2}{\sqrt{2}} x \Rightarrow y = \pm \sqrt{2} x$

Step 3. Graph of the equation

Graph of the equation is:

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

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

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In Problems 29–36, find the center, transverse axis, vertices, foci, and asymptotes. Graph each equation by hand. Verify your graph using a graphing utility.2x2-y2=4

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

Calculus

Mechanics Maths

Applied Mathematics

Discrete Mathematics

Pure Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

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