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