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Find the equation of all tangent lines at x = 0 to the curve x²y + y² = 2x + 1

Find the equation of all tangent lines at x = 0 to the curve x²y + y² = 2x + 1

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter3: Linear And Nonlinear Functions
Section: Chapter Questions
Problem 26MCQ
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Question
**Problem Statement:** Find the equation of all tangent lines at \( x = 0 \) to the curve \[ x^2 y + y^2 = 2x + 1 \] --- **Graph/Diagram Explanation:** No additional graphs or diagrams are provided in the image above. --- **Educational Context:** In this problem, you are given an implicit equation of a curve and you are asked to find the tangent lines at a specific point where \( x = 0 \). This is a common problem in calculus and involves differentiating implicitly to find the slope of the tangent lines at the given point. After finding the slope, you can use the point-slope form of a line to derive the equations of the tangent lines.
Transcribed Image Text:**Problem Statement:** Find the equation of all tangent lines at \( x = 0 \) to the curve \[ x^2 y + y^2 = 2x + 1 \] --- **Graph/Diagram Explanation:** No additional graphs or diagrams are provided in the image above. --- **Educational Context:** In this problem, you are given an implicit equation of a curve and you are asked to find the tangent lines at a specific point where \( x = 0 \). This is a common problem in calculus and involves differentiating implicitly to find the slope of the tangent lines at the given point. After finding the slope, you can use the point-slope form of a line to derive the equations of the tangent lines.
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