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

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)

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

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.

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| Find the product of length of tangent and length of normal for the curve y=x^(3)+3x^(2)+4x-1 at point x=0

The length of the normal to the curve y=a((e^(-x//a)+e^(x//a))/(2)) at any point varies as the

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

If a point P is moving such that the lengths of the tangents drawn form P to the circles x^(2) + y^(2) + 8x + 12y + 15 = 0 and x^(2) + y^(2) - 4 x - 6y - 12 = 0 are equal then find the equation of the locus of P