SOLUTION: Consider the graph of x^2+xy+y^2=1. Find all points where the tangent line is parallel to the line y = -x.

Algebra ->  Rational-functions -> SOLUTION: Consider the graph of x^2+xy+y^2=1. Find all points where the tangent line is parallel to the line y = -x.      Log On


   



Question 1027275: Consider the graph of x^2+xy+y^2=1. Find all points where the tangent line is parallel to the line y = -x.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
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Looks like the two positions marked in red are good candidates.
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Which would be the intersection of the ellipse and the line y=x.
Substituting,
x%5E2%2Bx%5E2%2Bx%5E2=1
3x%5E2=1
x%5E2=1%2F3
x=0+%2B-+1%2Fsqrt%283%29
y=0+%2B-+1%2Fsqrt%283%29
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