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`

The distance between the origin and the normal to the curve y=e^(2x)+x^2 at the point x = 0

Find the equation of the tangent and normal of the following curve at the specified point : y=x^(3)-3x at the point (2,2)

The tangent drawn at the point (0, 1) on the curve y=e^(2x) meets the x-axis at the point -

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

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

Find the equation of the tangent and normal of the following curves at the specified point: y=x^(2)+4x+1 at x=3

Find the equations of tangent and normal to the curve y(x-2)(x-3)-x+7=0 at the point where it meets the x-axis.

If p_(1) and p_(2) be the lengths of the perpendiculars from the origin upon the tangent and normal respectively to the curve x^((2)/(3)) +y^((2)/(3)) = a^((2)/(3)) at the point (x_(1), y_(1)) , then-

Find the equation of the tangent and the normal at the point (0, -1) to the curve 5x^2+3y^2+2x+4y+1=0

At any point on the curve 2x^2y^2-x^4=c , the mean proportional between the abscissa and the difference between the abscissa and the sub-normal drawn to the curve at the same point is equal to (a) ordinate (b) radius vector (c) x-intercept of tangent (d) sub-tangent