A normal at any point `(x , y)` to the curve `y=f(x)` cuts a triangle of unit area with the axis, the differential equation of the curve is

A normal at any point (x,y) to the curve y=f(x) cuts triangle of unit area with the axes,the equation of the curve is :

A curve y=f(x) has the property that the perpendicular distance of the origin from the normal at any point P of the curve is equal to the distance of the point P from the x-axis. Then the differential equation of the curve

The length of normal at any point to the curve,y=c cosh((x)/(c)) is

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 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.

A normal is drawn at a point P(x,y) of a curve.It meets the x-axis at Q. If PQ has constant length k, then show that the differential equation describing such curves is y(dy)/(dx)=+-sqrt(k^(2)-y^(2)). Find the equation of such a curve passing through (0,k).

If a curve is such that line joining origin to any point P (x,y) on the curve and the line parallel to y-axis through P are equally inclined to tangent to curve at P, then the differential equation of the curve is:

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