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`

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

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

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

Let P (h,K) be any point on curve y=f(x). Let tangent drawn at point P meets x-axis at T & normal at point P meets x-axis at N (as shown in figure) and m =(dy)/(dx)]_()(h,k)) = shope of tangent. (i) Length of tangent =PT =|K| sqrt(1+(1)/(m^(2))) (ii) Length of Normal =PN + |K| sqrt(1+m^(2)) (iii) Length subtangent = Projection of segment PT on x-axis =TM =|(k)/(m)| (iv) Length of subnormal =Projection of line segment PN on x-axis =MN =|Km| Determine 'p' such that the length of the subtangent and subnormal is equal for the curve y=e^(px) +px at the point (0,1)

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

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