Find the family of curves, the subtangent at any point of which is the arithmetic mean of the co-ordinate point of tangency.

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.

For the curve y=a ln(x^(2)-a^(2)), show that the sum of length of tangent and sub-tangent at any point is proportional to product of coordinates of point of tangency.

The length of the subtangent at any point on the curve y=be^(x/3) is

Show that equation to the curve such that the y-intercept cut off by the tangent at an arbitrary point is proportional to the square of the ordinate of the point of tangency is of the form a/x+b/y=1 .

Show that equation to the curve such that the y-intercept cut off by the tangent at an arbitrary point is proportional to the square of the ordinate of the point of tangency is of the form a/x+b/y=1 .

A conic passes through the point (2,4) and is such that the segment of any of its tangents at any point contained between the co-ordinate axes is bisected at the point of tangency.Then the foci of the conic are:

The Curve possessing the property text the intercept possessing the property text the intercept made by the tangent at any point of the curve on they-axis is equal to square of the abscissa of the point of tangency,is given by

Cartesian Co-ordinate of a point

The subtangent at any point on the curve x^(m)y^(n)=a^(m+n) varies as