
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Please show all work and steps clearly. The format and steps have not always been clear. Thank you.
![**Problem Statement:**
Find the equation of the tangent line to the curve (a lemniscate)
\[ 2(x^2 + y^2)^2 = 25(x^2 - y^2) \]
at the point \((3, -1)\).
**Solution Format:**
The equation of this tangent line can be written in the form \( y = mx + b \)
**Where:**
\( m \) is: [Blank space for students to fill]
\( b \) is: [Blank space for students to fill]
**Instructions:**
- Calculate the derivative of the given lemniscate equation to find the slope \( m \) at the point \((3, -1)\).
- Use the point-slope form to determine the y-intercept \( b \) once the slope \( m \) is known.
- Provide your final answer in the format \( y = mx + b \) filling in the blanks provided.](https://content.bartleby.com/qna-images/question/1dbff557-c987-45fc-8dd6-6084416c9157/16a9030e-c33d-4fdb-b0fc-796239144971/90gutk_thumbnail.png)
Transcribed Image Text:**Problem Statement:**
Find the equation of the tangent line to the curve (a lemniscate)
\[ 2(x^2 + y^2)^2 = 25(x^2 - y^2) \]
at the point \((3, -1)\).
**Solution Format:**
The equation of this tangent line can be written in the form \( y = mx + b \)
**Where:**
\( m \) is: [Blank space for students to fill]
\( b \) is: [Blank space for students to fill]
**Instructions:**
- Calculate the derivative of the given lemniscate equation to find the slope \( m \) at the point \((3, -1)\).
- Use the point-slope form to determine the y-intercept \( b \) once the slope \( m \) is known.
- Provide your final answer in the format \( y = mx + b \) filling in the blanks provided.
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