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.

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.

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

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.

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 .

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.

Find the equation of the straight lines which cut off an intercept 4 from the y-axis and are equally inclined to the axes.

Find the equation of the straight lines which cut off an intercept 5 from the y-axis and are equally inclined to the axes.

Find the equation of the curve which is such that the area of the rectangle constructed on the abscissa of any point and the intercept of the tangent at this point on the y-axis is equal to 4.