If the length of the sub-tangent at any point to the curve `xy^(n)=a` is proportional to the abscissa,then `n` is

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

A curve y=f(x) passes through point P(1,1). The normal to the curve at P is a (y-1)+(x-1)=0. If the slope of the tangent at any point on the curve is proportional to the ordinate of the point,then the equation of the curve is

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

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 the tangency square root of the absissa of the point of tangency cube of the abscissa of the point of tangency cube root of the abscissa of the point of tangency

A curve is such that the length of perpendicular from origin on the tangent at any point P of the curve is equal to the abscissa of P . Prove that the differential equation of the curve is y^2-2xy dy/dx-x^2=0 and hence find the curve.

The value of n for which the length of the sub- normal at any point of the curve y^(3)=a^(1-n)x^(2n) must be constant is

Find the curve for which the sum of the lengths of the tangent and subtangent at any of its point is proportional to the product of the co-ordinates of the point of tangency, the proportionality factor is equal to k.

The perpendicular from the origin to the tangent at any point on a curve is equal to the abscissa of the point of contact. Find the equation of the curve satisfying the above condition and which passes through (1, 1).

The curve is such that the length of the perpendicular from the origin on the tangent at any point P of the curve is equal to the abscissa of Pdot Prove that the differential equation of the curve is y^2-2x y(dy)/(dx)-x^2=0, and hence find the curve.