document.write( "Question 1010151: Find the equation of the tangent line to the curve (x-y)^2=2x+1 at the point (4,1). \n" ); document.write( "

Algebra.Com's Answer #631447 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"x%5E2-2xy%2By%5E2=2x%2B1\"$
\n" ); document.write( "Differentiate implicitly.
\n" ); document.write( " $\"2xdx-%282xdy%2B2ydx%29%2B2ydy=2dx\"$
\n" ); document.write( " $\"%28-2x%2B2y%29dy=%282y-2x%2B2%29dx\"$
\n" ); document.write( " $\"dy%2Fdx=%282y-2x%2B2%29%2F%282y-2x%29\"$
\n" ); document.write( " $\"dy%2Fdx=%28y-x%2B1%29%2F%28y-x%29\"$
\n" ); document.write( "So at (4,1),
\n" ); document.write( " $\"m=dy%2Fdx=%281-4%2B1%29%2F%281-4%29=%28-2%29%2F%28-3%29\"$
\n" ); document.write( " $\"m=2%2F3\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"y-1=%282%2F3%29%28x-4%29\"$
\n" ); document.write( " $\"y-1=%282%2F3%29x-8%2F3\"$
\n" ); document.write( " $\"y=%282%2F3%29x-8%2F3%2B3%2F3\"$
\n" ); document.write( " $\"highlight%28y=%282%2F3%29x-5%2F3%29\"$
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