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.

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 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 equation of the curve in which the perpendicular from the origin on any tangent is equal to the abscissa of the point of contact.

The curve for which the slope of the tangent at any point is equal to the ration of the abcissa to the ordinate of the point 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 .

Find the intercepts cut off by the plane 2x + y- z = 5 .

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

The curve y=f(x) in the first quadrant is such that the y - intercept of the tangent drawn at any point P is equal to twice the ordinate of P If y=f(x) passes through Q(2, 3) , then the equation of the curve is

The x intercept of the tangent to a curve f(x,y) = 0 is equal to the ordinate of the point of contact. Then the value of (d^(2)x)/(dy^(2)) at the point (1,1) on the curve is "_____".

Find the curve for which area of triangle formed by x-axis, tangent drawn at any point on the curve and radius vector of point of tangency is constant, equal to a^2