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Chapter 10: Q. 38 (page 668)

In Problems 37–40, write an equation for each hyperbola.

Short Answer

Expert verified

Equation of hyperbola is: $y^{2} - x^{2} = 1$

Step by step solution

01

Step 1. Given information

Graph of the hyperbola:

02

Step 2. Finding the equation of hyperbola

Comparing information from the graph with standard form of hyperbola,

$Vertices = (0, \pm 1) = (0, \pm a) Asymptotes = \pm x = \pm \frac{a}{b} x \Rightarrow a = 1, b = 1$

Equation of hyperbola is:

localid="1647139411863" $\frac{y^{2}}{1^{2}} - \frac{x^{2}}{1^{2}} = 1 \Rightarrow y^{2} - x^{2} = 1$

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Most popular questions from this chapter

In Problems 15–18, the graph of a hyperbola is given. Match each graph to its equation.

Equations:

$(A) \frac{x^{2}}{4} - y^{2} = 1 (B) x^{2} - \frac{y^{2}}{4} = 1 (C) \frac{y^{2}}{4} - x^{2} = 1 (D) y^{2} - \frac{x^{2}}{4} = 1$

Graph:

Use the Square Root Method to find the real solutions of ${(x + 4)}^{2} = 9$ .

In Problems 15–18, the graph of a hyperbola is given. Match each graph to its equation.

Equations:

$(A) \frac{x^{2}}{4} - y^{2} = 1 (B) x^{2} - \frac{y^{2}}{4} = 1 (C) \frac{y^{2}}{4} - x^{2} = 1 (D) y^{2} - \frac{x^{2}}{4} = 1$

Graph:

To transform the equation

$A x^{2} + B x y + C y^{2} + D x + E y + F = 0, B \neq 0$

into one in $x'$ and $y'$ without an $x' y' -$ term, rotate the axes

through an acute angle $θ$ that satisfies the equation _______.

True or False

The equation $3 x^{2} + B x y + 12 y^{2} = 10$ defines a parabola if $B = - 12$ .

See all solutions

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