Basic Curves #!#Area with Axis

The tangent at a point P of a curve meets the y-axis at A, and the line parallel to y-axis at A, and the line parallel to y-axis through P meets the x-axis at B. If area of DeltaOAB is constant (O being the origin), Then the curve is

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

Find the area enclosed the curve y=sin x and the X-axis between x=0 and x=pi .

The area of the triangle formed by the tangent to the curve xy=a^(2) at any point on the curve with the coordinate axis is

The largest area of a rectangle which has one side on the x-axis and the two vertices on the curve y=e^(-x^(2) is

The largest area of a rectangle which has one side on the x-axis and the two vertices on the curve y=e^(-x^(2)) is