The curve for which the ratio of the length of the segment intercepted by any tangent on the Y-axis to the length of the radius vector is constant `(k),` is

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 curve for which the length of the normal is equal to the length of the radius vector is/are (a) circles (b) rectangular hyperbola (c) ellipses (d) straight lines

The curve for which the length of the normal is equal to the length of the radius vector is/are (a) circles (b) rectangular hyperbola (c) ellipses (d) straight lines

Find all the curves y=f(x) such that the length of tangent intercepted between the point of contact and the x-axis is unity.

Find the curve for which the perpendicular from the foot of the ordinate to the tangent is of constant length.

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 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

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.

Find the curve for which the length of normal is equal to the radius vector.