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.

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

For the curve y=a1n(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.

For the curve y=a1n(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 equation of all possible curves such that length of intercept made by any tangent on x-axis is equal to the square of X-coordinate of the point of tangency. Given that the curve passes through (2,1)

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

The Curve possessing the property that 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

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

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

Find the equation of the curve passing through origin if the slope of the tangent to the curve at any point (x ,y)i s equal to the square of the difference of the abscissa and ordinate of the point.