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Question

Find the equation of the tangent to the curve y=3x-2 which is parallel to the 4x − 2y + 5 = 0.

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Solution

Slope of the given line is 2
Let x1,y1be the point where the tangent is drawn to the curve y=3x-2Since, the point lies on the curve.Hence, y1=3x1-2 ... 1Now, y=3x-2dydx=323x-2Slope of tangent at x1,y1 =323x1-2Given thatSlope of tangent = slope of the given line323x1-2=23=43x1-29=163x1-2916=3x1-23x1=916+2=9+3216=4116x1=4148Now, y1=12348-2=2748=916=34 From (1)x1, y1=4148, 34Equation of tangent is,y-y1=m x-x1y-34=2 x-41484y-34=248x-414824y-18=48x-4148x-24y-23=0

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