Math Problem Statement

final answer only

The line that is normal to the curve x^2 + xy - 2y^2 = 0 at (5,5) intersects the curve at what other point?

Solution

The other point where the line normal to the curve x2+xy−2y2=0x^2 + xy - 2y^2 = 0 at (5,5)(5, 5) intersects is:

(−5,−5)(-5, -5).

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Math Problem Analysis

Mathematical Concepts

Analytic Geometry
Implicit Differentiation
Normal Line

Formulas

Implicit differentiation
Slope of a tangent line
Equation of a normal line

Theorems

The slope of the normal is the negative reciprocal of the tangent slope

Suitable Grade Level

Grades 11-12 or Early College

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