Find the equation of the hyperbola shown below. Q Q 1₁--9- 17 ਰਿਹਾ ਹੈ What is the equation for this hyperbola? Select the correct choice and complete the answer boxes to complete your choice. ₂² 2 4 36 A. OB. v² 2 =1

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
icon
Related questions
Question

A step-by-step would help!

The task is to find the equation of the hyperbola shown in the graph. The graph on the left features a set of coordinate axes with a hyperbola drawn in red. The asymptotes are depicted in blue dashed lines, forming diagonals through the center at the origin.

### Graph Details:
- The hyperbola opens horizontally.
- Asymptotes intersect at the origin (0,0) and have lines passing through the graph with equations resembling \( y = \pm \frac{b}{a} x \), where a and b are constants related to the hyperbola's equation.
- X-axis and Y-axis range from -12 to 12.

### Equation Selection:
On the right is a multiple-choice question with two options for the equation of the hyperbola:

A. \(\frac{x^2}{4} - \frac{y^2}{36} = 1\)

B. \(\frac{y^2}{\Box} - \frac{x^2}{\Box} = 1\)

The correct option is indicated as A: \(\frac{x^2}{4} - \frac{y^2}{36} = 1\).

This equation matches the graph's hyperbola orientation and structure, with the transverse axis along the x-axis and reflecting the characteristics depicted in the graph.
Transcribed Image Text:The task is to find the equation of the hyperbola shown in the graph. The graph on the left features a set of coordinate axes with a hyperbola drawn in red. The asymptotes are depicted in blue dashed lines, forming diagonals through the center at the origin. ### Graph Details: - The hyperbola opens horizontally. - Asymptotes intersect at the origin (0,0) and have lines passing through the graph with equations resembling \( y = \pm \frac{b}{a} x \), where a and b are constants related to the hyperbola's equation. - X-axis and Y-axis range from -12 to 12. ### Equation Selection: On the right is a multiple-choice question with two options for the equation of the hyperbola: A. \(\frac{x^2}{4} - \frac{y^2}{36} = 1\) B. \(\frac{y^2}{\Box} - \frac{x^2}{\Box} = 1\) The correct option is indicated as A: \(\frac{x^2}{4} - \frac{y^2}{36} = 1\). This equation matches the graph's hyperbola orientation and structure, with the transverse axis along the x-axis and reflecting the characteristics depicted in the graph.
Expert Solution
Step 1

To determine the equation of given hyperbola.

steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education