Chapter 11: Q. 3 (page 772)

Graph the equation: $y^{2} = x^{2} - 1$

Short Answer

Expert verified

The graph of $y^{2} = x^{2} - 1$ is

Step by step solution

Step 1. Give data

The given equation is

$y^{2} = x^{2} - 1$

Step 2. Properties of equation

Rearrange the equation into the standard form of the equation of the hyperbola

$y^{2} = x^{2} - 1 \frac{x^{2}}{1^{2}} - \frac{y^{2}}{1^{2}} = 1 \frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$

so $a = 1 b = 1 c = \sqrt{a^{2} + b^{2}} c = \sqrt{2}$

vertices are localid="1646864511684" $(\pm a, 0) = (\pm 1, 0)$

foci are $(0, \pm c) = (0, \pm \sqrt{2})$

Step 3. Graph

Plot a hyperbola of the vertices $(\pm 1, 0)$ and foci $(0, \pm \sqrt{2})$ to plot the graph of $y^{2} = x^{2} - 1$

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Graph the equation: $y^{2} = x^{2} - 1$

Short Answer

Step by step solution

Step 1. Give data

Step 2. Properties of equation

Step 3. Graph

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Graph the equation:y2=x2-1

Short Answer

Step by step solution

Step 1. Give data

Step 2. Properties of equation

Step 3. Graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Discrete Mathematics

Decision Maths

Calculus

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Graph the equation: $y^{2} = x^{2} - 1$