At any point on the curve `y=f(x)` ,the sub-tangent, the ordinate of the point and the sub-normal are in

Prove that for the curve y=be^(x//a) , the subtangent is of constant length and the sub-normal varies as the square of the ordinate .

If the least area of triangle formed by tangent,normal at any point P on the curve y=f(x) and X -axis is 4sq. unit.Then the ordinate of the point P(P lies in first quadrant) is

At any point on the curve y=f(x), the length of the sub normal is constant, then the curve is

A curve y=f(x) passes through point P(1,1). The normal to the curve at P is a (y-1)+(x-1)=0. If the slope of the tangent at any point on the curve is proportional to the ordinate of the point,then the equation of the curve is

A curve y=f(x) passes through the point P(1,1) . The normal to the curve at P is a(y-1)+(x-1)=0 . If the slope of the tangent at any point on the curve is proportional to the ordinate of the point. Determine the equation of the curve. Also obtain the area bounded by the y-axis, the curve and the normal to the curve at P .

If length of tangent at any point on the curve y=f(x) intercepted between the point and the x -axis is of length l. Find the equation of the curve.

If the length of sub-normal is equal to the length of sub-tangent at any point (3,4) on the curve y=f(x) and the tangent at (3,4) to y=f(x) meets the coordinate axes at A and B ,then the maximum area of the triangle OAB, where O is origin,is 45/2 (b) 49/2(c) 25/2 (d) 81/2

If length of tangent at any point on th curve y=f(x) intercepted between the point and the x -axis is of length 1. Find the equation of the curve.

Find the point on the curve y=x^(2) , where the slope of the tangent is equal to the x co-ordinate of the point.