Find The Equations Of The Tangent Lines To The Cur

Anonymous

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Find the equations of the tangent lines to the curve y = (x-1)/(x+1) that are parallel to the line x-2y = 1.

 

Answer No.1

SmartSam82

From: US
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From x-2y = 1, y = (1/2)x - 1/2, and Since parallel lines will have same slope, slope of given line and tangent line = 1/2 y' = (x+1) - (x-1) /(x+1)^2 = 2/(x+1)^2 2/(x+1)^2 = 1/2 (x+1)^2 = 4 x^2 + 2x - 3 = 0 (x + 3)(x-1) = 0 x = -3 or 1 so plug in y(-3) = (-3-1)/(-3+1) = -4/-2 = 2 y(1) = 0 so point of tangency = (-3,2) and (1,0) eqns of tangent line are y -2 = (1/2)(x + 3) and (y - 0) = (1/2)(x - 1) y - 2 = x/2 + 3/2 and y = x/2 - 1/2 y = (1/2)x + 7/2 y = (1/2)x - 1/2

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