Homework Help is Here – Start Your Trial Now!
Math
Calculus
x + 2x – 3, that is also parallel to Find the equation of the normal line to the parabola y – 2x + 2y = 9. 15 y = x + 4

x + 2x – 3, that is also parallel to Find the equation of the normal line to the parabola y – 2x + 2y = 9. 15 y = x + 4

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
See similar textbooks
icon
Related questions
Question
**Problem Statement:** Find the equation of the normal line to the parabola \( y = x^2 + 2x - 3 \) that is also parallel to \( -2x + 2y = 9 \). **Solution Attempt:** \[ y = x + \frac{15}{4} \] **Feedback:** The given solution is incorrect, as marked by the red cross. --- **Explanation:** This problem involves finding the equation of a normal line to a given parabola that is parallel to a specific line equation. 1. **Understanding the Parabola:** - The parabola equation is \( y = x^2 + 2x - 3 \). - The derivative, \( \frac{dy}{dx} = 2x + 2 \), gives the slope of the tangent at any point on the parabola. 2. **Normal Line Slope:** - The slope of the normal line is the negative reciprocal of the tangent slope. 3. **Parallel Line Condition:** - Line \( -2x + 2y = 9 \) can be rearranged to standard form: \( y = x + \frac{9}{2} \). - The slope is 1. So, the normal line must parallel a line with slope 1, meaning its slope is the same. 4. **Conclusion:** - The attempted solution did not correctly align with these criteria.
Transcribed Image Text:**Problem Statement:** Find the equation of the normal line to the parabola \( y = x^2 + 2x - 3 \) that is also parallel to \( -2x + 2y = 9 \). **Solution Attempt:** \[ y = x + \frac{15}{4} \] **Feedback:** The given solution is incorrect, as marked by the red cross. --- **Explanation:** This problem involves finding the equation of a normal line to a given parabola that is parallel to a specific line equation. 1. **Understanding the Parabola:** - The parabola equation is \( y = x^2 + 2x - 3 \). - The derivative, \( \frac{dy}{dx} = 2x + 2 \), gives the slope of the tangent at any point on the parabola. 2. **Normal Line Slope:** - The slope of the normal line is the negative reciprocal of the tangent slope. 3. **Parallel Line Condition:** - Line \( -2x + 2y = 9 \) can be rearranged to standard form: \( y = x + \frac{9}{2} \). - The slope is 1. So, the normal line must parallel a line with slope 1, meaning its slope is the same. 4. **Conclusion:** - The attempted solution did not correctly align with these criteria.
Expert Solution
Step 1

  Definition used -

                        Slope of normal - The slope of normal at a point is the negative reciprocal of the slope of the tangent at that point.

                       The slope of normal for function f(x) at x = a can be found by the given formula -

                                                      m=-1f'(a)

                       

                                    

steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Implicit Differentiation
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS