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

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

The x-intercept of the tangent at any arbitrary point of the curve a/(x^2)+b/(y^2)=1 is proportional to square of the abscissa of the point of tangency square root of the abscissa of the point of tangency cube of the abscissa of the point of tangency cube root of the abscissa of the point of tangency

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

A particle moves along the curve y^(2) = 8x . At what point on the curve do the abscissa and ordinate increase at the same rate?

For the curve x^(2)+4xy+8y^(2)=64 , the tangents are parallel to the x-axis only at the points-

For the curve x^(2)+4xy+8y^(2)=64 the tangents are parallel to the x-axis only at the points

For the curve x y=c , prove that the portion of the tangent intercepted between the coordinate axes is bisected at the point of contact.

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)

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 the tangent and normal to the curve y=x^2-4x-5 at x= -2.