Curve `C_1\ : y=e x\ ln\ x\ a n d\ C_2: y=(lnx)/(e x)\ ` intersect at point ` p ` whose abscissa is less than `1` . Find equation of normal to curve `C_1` at point `P` .

Curve C_(1):y=ex ln x and C_(2):y=(ln x)/(ex) intersect at point 'p' whose abscissa is less than 1. Find equation of normal to curve C_(1) at point P.

Find the equation of normal to the curve, y = .x^3 at the point (1,1).

Find the equation of the normal to the curve y = x^3 at the point (2,1).

Find the equation of normal to the curve, y = .x^3 at the point (-1.-1).

The equation of normal to the curve y=x^(3)-x^(2)-1 at the point whose abscissa is -2, is

Find the equations of the tangent and normal to the curve y= (log x)^2 at point x = 1/e .

The equation of normal to the curve y = log_(e) x at the point P( 1, 0) is ..... .

Find the equation of the tangent to the curve y=x log_e x + 2 at the point (1, 2).

Let C : x^(2) + y^(2) = 9, E : (x^(2))/(9) + (y^(2))/(4) =1 and L : y = 2x be three curves P be a point on C and PL be the perpendicular to the major axis of ellipse E. PL cuts the ellipse at point M. If equation of normal to C at point P be L : y = 2x then the equation of the tangent at M to the ellipse E is