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`.

Find the curve for which the intercept cut off by any tangent on y-axis is proportional to the square of the ordinate of the point of tangency.

Find the equation of the curve such that the square of the intercept cut off by any tangent from the y-axis is equal to the product of the co-ordinate of the point of tangency.

The equation of the curve which is such that the portion of the axis of x cut off between the origin and tangent at any point is proportional to the ordinate of that point is

The equation of the curve which is such that the portion of the axis of x cut-off between the origin and tangent at any point is proportional to the ordinate of that point is

Find the curve for which the intercept cut off by a tangent on x-axis is equal to four xx the ordinate of the point of contact.

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.

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.

A curve passing through (1,0) is such that the ratio of the square of the intercept cut by any tangent on the y-axis to the Sub-normal is equal to the ratio of the product of the coordinates of the point of tangency to the product of square of the slope of the tangent and the subtangent at the same point,is given by

At any point on the curve (a)/(x^(2))+(b)/(y^(2))=1, the y-intercept made by the tangent is proportional to