The equation of the normal to the curve y=x x , which is parallel to the line 2 x-2 y+3=0 , is

Step-by-step solution

y=x x Differentiating w.r.to x , we get d y ~d x =1+ x Slope of tangent =1+ x Slope of given line =1 Line of normal is parallel to given line aligned & d y ~d x =-1 & 1+ x=-1 & x=-2 & x= e ⁻² aligned Substituting x= e ⁻² in given equation, aligned y & =x x & = e ⁻² e ⁻² & =-2 e ⁻² aligned Equation of line passing through ( e ⁻²,-2 e ⁻² ) is aligned & y+2 e ⁻²=1 (x- e ⁻² ) & x-y=3 e ⁻² aligned