Find The Equation Tangent Line To Given Curve At P

Anonymous

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Find the equation tangent line to given curve at points (2,1): x^2 + 4xy + y^2 = 13

 

Answer No.1

CrazyMath

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X2 + 4xy + y2 = 13 => d / dx ( x2 + 4xy + y2 ) = d / dx ( 13 ) => 2x + 4y + 4xy' + 2yy' = 0 => 4xy' + 2yy' = - ( 2x + 4y) => ( 4x + 2y )y' = - ( 2x + 4y) => y' = - ( 2x + 4y ) / ( 4x + 2y) => y' = - ( x + 2y ) / ( 2x + y) The slope of the line tangent to the curve at the point ( 2, 1 )is: m = y'( 2, 1 ) = - ( 2 + 2 ) /( 4 + 1 ) = -4 / 5 The equation of the tangent line is: yt = ( -4 / 5 )x + b yt( 2 ) = 1 => -8 / 5 + b = 1 => b = 5 / 5 + 8 / 5 => b = 13 / 5 => yt = ( -4 / 5 )x + 13 / 5

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