Determine `p` such that the length of the such-tangent and sub-normal is equal for the curve `y=e^(p x)+p x` at the point `(0,1)dot`

If L_(T), L_(N), L_(ST) and L_(SN) denote the lengths of tangent, normal, sub-langent and sub-normal respectively, ofa curve y =f(x) at a point P (2009, 2010) on it, then

If the length of the sub tangent is 9 and the length of the sub normal is 4 at (x, y) on y=f(x) then |y|=

Find the length of sub-tangent to the curve y=e^(x/a)

The length of tangent at a point P(x_(1),y_(1)) to the curve y=f(x) ,having slope m at P is

The area bounded by the coordinate axes and normal to the curve y=log_(e)x at the point P( 1 , 0), is

The ratio of the length of tangent to the length of normal to the curve y=3e^(5x) at the intersection point of curve and y -axis is

The ratio of the length of tangent to the length of normal to the curve y=3e^(5x) at the intersection point of curve and y-axis is