Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Sketch the level curves of the function f(x, y) = - y² for c= -4,-1, 0, 1, 4. 9

Sketch the level curves of the function f(x, y) = - y² for c= -4,-1, 0, 1, 4. 9

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
**Sketch the level curves** of the function \( f(x, y) = \frac{x^2}{9} - y^2 \) for \( c = -4, -1, 0, 1, 4 \). **Graph Explanation:** The image shows a coordinate plane with both the x-axis and y-axis ranging from -8 to 8. The grid lines are divided into one-unit increments. This blank coordinate plane is used to sketch the level curves of the given function for different values of \( c \). Each level curve represents the set of points \((x, y)\) that satisfies the equation \( \frac{x^2}{9} - y^2 = c \) for a specific value of \( c \). To sketch these curves: 1. **For \( c = -4 \):** This value will typically result in hyperbolas opening along the y-axis. 2. **For \( c = -1 \):** Similar to \( c = -4 \), expect hyperbolas opening along the y-axis. 3. **For \( c = 0 \):** This will represent the degenerate case, usually a pair of intersecting lines. 4. **For \( c = 1 \):** Expect hyperbolas opening along the x-axis. 5. **For \( c = 4 \):** Similar to \( c = 1 \), hyperbolas opening along the x-axis. Each curve will illustrate how the function \( f(x, y) \) behaves for different constant outputs.
Transcribed Image Text:**Sketch the level curves** of the function \( f(x, y) = \frac{x^2}{9} - y^2 \) for \( c = -4, -1, 0, 1, 4 \). **Graph Explanation:** The image shows a coordinate plane with both the x-axis and y-axis ranging from -8 to 8. The grid lines are divided into one-unit increments. This blank coordinate plane is used to sketch the level curves of the given function for different values of \( c \). Each level curve represents the set of points \((x, y)\) that satisfies the equation \( \frac{x^2}{9} - y^2 = c \) for a specific value of \( c \). To sketch these curves: 1. **For \( c = -4 \):** This value will typically result in hyperbolas opening along the y-axis. 2. **For \( c = -1 \):** Similar to \( c = -4 \), expect hyperbolas opening along the y-axis. 3. **For \( c = 0 \):** This will represent the degenerate case, usually a pair of intersecting lines. 4. **For \( c = 1 \):** Expect hyperbolas opening along the x-axis. 5. **For \( c = 4 \):** Similar to \( c = 1 \), hyperbolas opening along the x-axis. Each curve will illustrate how the function \( f(x, y) \) behaves for different constant outputs.
Expert Solution
Step 1: Introduction of the given problem

We have to sketch the level curve of f open parentheses x comma y close parentheses equals x squared over 9 minus y squared for c equals negative 4 comma negative 1 comma 0 comma 1 comma 4

steps

Step by step

Solved in 3 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS