Math Problem Statement

a. Determine an equation of the tangent line and the normal line at the given point on the curve. b. Graph the tangent and normal lines on the given graph. 11 left parenthesis x squared plus y squared right parenthesis squared equals 3721 left parenthesis x squared minus y squared right parenthesis11x2+y22=3721x2−y2​; left parenthesis 6 comma 5 right parenthesis(6,5)

Solution

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Math Problem Analysis

Mathematical Concepts

Implicit Differentiation
Tangent Line
Normal Line
Geometry of Curves

Formulas

(x^2 + y^2)^2 = 3721(x^2 - y^2)
Point-Slope form of the line: y - y1 = m(x - x1)
Slope of normal line: m_normal = -1/m_tangent

Theorems

Implicit Differentiation Theorem
Perpendicular Line Theorem

Suitable Grade Level

Grades 11-12