Find the equation of a normal to the curve y = x loge x which is parallel to the line
2x – 2y + 3 = 0.

finding the slope of the tangent by differentiating the curve



m(tangent) =


normal is perpendicular to tangent so, m1m2 = – 1


m(normal) =


equation of normal is given by y – y1 = m(normal)(x – x1)


now comparing the slope of normal with the given equation


m(normal) = 1




since this point lies on the curve, we can find y by substituting x



The equation of normal is given by



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