document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #642613 by Fombitz(32388) $\"\"$ $\"About$

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\n" ); document.write( "Looks like the two positions marked in red are good candidates.
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\n" ); document.write( "Which would be the intersection of the ellipse and the line $\"y=x\"$ .
\n" ); document.write( "Substituting,
\n" ); document.write( " $\"x%5E2%2Bx%5E2%2Bx%5E2=1\"$
\n" ); document.write( " $\"3x%5E2=1\"$
\n" ); document.write( " $\"x%5E2=1%2F3\"$
\n" ); document.write( " $\"x=0+%2B-+1%2Fsqrt%283%29\"$
\n" ); document.write( " $\"y=0+%2B-+1%2Fsqrt%283%29\"$
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