document.write( "Question 554379: Find the equations of the tangent line and normal line to the graph of 6x^2-2xy+y^3=9 at the point (2,-3) \n" ); document.write( "

Algebra.Com's Answer #361320 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "6x² - 2xy + y³ = 9\r\n" );
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document.write( "Find the derivative implicitly term by term:\r\n" );
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document.write( "12x - 2(x + y) + 3y² = 0\r\n" );
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document.write( "Solve for \r\n" );
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document.write( "12x - 2x - 2y + 3y² = 0\r\n" );
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document.write( "Isolate the terms in  \r\n" );
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document.write( "-2x + 3y² = -12x + 2y\r\n" );
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document.write( "(-2x + 3y²) = -12x + 2y\r\n" );
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document.write( " = \r\n" );
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document.write( "Write the positive terms first\r\n" );
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document.write( " = \r\n" );
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document.write( " =  =  =  =  = \r\n" );
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document.write( "Finding the tangent line is the algebra problem of finding the equation \r\n" );
document.write( "of the line through the point (2,-3) with a slope of \r\n" );
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document.write( "The equation of the tangent line at (2,-3) is\r\n" );
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document.write( "y = x - \r\n" );
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document.write( "Finding the normal line is the algebra problem of finding the equation \r\n" );
document.write( "of the line through the point (2,-3) with a slope of \r\n" );
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document.write( "The equation of the normal line at (2,-3) is\r\n" );
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document.write( "y = x - \r\n" );
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document.write( "Edwin

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