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` .

The equation of normal to the curve y= x ^(2) + 2 at point (1,1) is :

Equation of the normal to the curve y=-sqrt(x)+2 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

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

The equation of normal to the curve x^(2)+y^(2)-3x-y+2=0 at P(1,1) is

Find the equation of tangent and normal to the curve y =3x^(2) -x +1 at the point (1,3) on it.

Let C : x^(2) + y^(2) = 9, E : (x^(2))/(9) + (x^(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

In the curve y=ce^((x)/(a)), the sub-tangent is constant sub-normal varies as the square of the ordinate tangent at (x_(1),y_(1)) on the curve intersects the x-axis at a distance of (x_(1)-a) from the origin equation of the normal at the point where the curve cuts y-axis is cy+ax=c^(2)

Find the equations of the tangent and the normal to the curve y^2=4a x at (x_1,\ y_1) at indicated points.

A curve C passes through origin and has the property that at each point (x,y) on it the normal line at that point passes through (1,0) The equation of a common tangent to the curve C and the parabola y^(2)=4x is