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^(p x)+p x at the point (0,1)dot

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)

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

Find the length of the tangent for the curve y=x^3+3x^2+4x-1 at point x=0.

Find the length of the tangent for the curve y=x^3+3x^2+4x-1 at point x=0.

The length of the Sub tangent at (2,2) to the curve x^5 = 2y^4 is

The curve y=f(x) in the first quadrant is such that the y - intercept of the tangent drawn at any point P is equal to twice the ordinate of P If y=f(x) passes through Q(2, 3) , then the equation of the curve is

If the length of sub-normal is equal to the length of sub-tangent at any point (3,4) on the curve y=f(x) and the tangent at (3,4) to y=f(x) meets the coordinate axes at Aa n dB , then the maximum area of the triangle O A B , where O is origin, is 45/2 (b) 49/2 (c) 25/2 (d) 81/2

If the length of sub-normal is equal to the length of sub-tangent at any point (3,4) on the curve y=f(x) and the tangent at (3,4) to y=f(x) meets the coordinate axes at Aa n dB , then the maximum area of the triangle O A B , where O is origin, is 45/2 (b) 49/2 (c) 25/2 (d) 81/2

Tangent and normal at any point P of the parabola y^(2)=4ax(a gt 0) meet the x-axis at T and N respectively. If the lengths of sub-tangent and sub-normal at this point are equal, then the area of DeltaPTN is given by