A tangent at a point P on the curve cuts the x-axis at A and B is the foot of perpendicular from P on the x axis. If the midpoint of AB is fixed at `(alpha,0)` for any point P, find the differential equation and hence find the curve.

If the tangent at any point P of a curve meets the axis of X in T find the curve for which O P=P T ,O being the origin.

Let y=f(x)be curve passing through (1,sqrt3) such that tangent at any point P on the curve lying in the first quadrant has positive slope and the tangent and the normal at the point P cut the x-axis at A and B respectively so that the mid-point of AB is origin. Find the differential equation of the curve and hence determine f(x).

Let y=f(x)be curve passing through (1,sqrt3) such that tangent at any point P on the curve lying in the first quadrant has positive slope and the tangent and the normal at the point P cut the x-axis at A and B respectively so that the mid-point of AB is origin. Find the differential equation of the curve and hence determine f(x).

Let y=f(x)be curve passing through (1,sqrt3) such that tangent at any point P on the curve lying in the first quadrant has positive slope and the tangent and the normal at the point P cut the x-axis at A and B respectively so that the mid-point of AB is origin. Find the differential equation of the curve and hence determine f(x).

Let y=f(x)be curve passing through (1,sqrt3) such that tangent at any point P on the curve lying in the first quadrant has positive slope and the tangent and the normal at the point P cut the x-axis at A and B respectively so that the mid-point of AB is origin. Find the differential equation of the curve and hence determine f(x).

If the tangent at any point P of a curve meets the axis of x in T. Then the curve for which OP=PT,O being the origins is

If the tangent at any point P of a curve meets the axis of x in T. Then the curve for which OP=PT,O being the origins is

The point P (5, 3) was reflected in the origin to get the image P'. If N is the foot of the perpendicular from P' to the x-axis, find the co-ordinates of N.

The point P (5, 3) was reflected in the origin to get the image P'. If M is the foot of the perpendicular from P to the x - axis , find the co-ordinates of M.

If the tangent at any point P of a curve meets the axis of XinTdot find the curve for which O P=P T ,O being the origin.