A curve `y=f(x)` passes through the origin. Through any point `(x , y)` on the curve, lines are drawn parallel to the co-ordinate axes. If the curve divides the area formed by these lines and co-ordinates axes in the ratio `m : n ,` find the curve.

A curve y=f(x) passing through origin and (2,4). Through a variable point P(a,b) on the curve,lines are drawn parallel to coordinates axes.The ratio of area formed by the curve y=f(x),x=0,y=b to the area formed by the y=f(x),y=0,x=a is equal to 2:1. Equation of line touching both the curves y=f(x) and y^(2)=8x is

Find the equation of lines drawn parallel to co-ordinate axes and passing through the point (-1,4) .

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 :

Co-ordinates of a point on the curve y=x log s at which at normal is parallel to the line 2x-2y=3 are

What is the area between the curve y = cos 3x, 0 le x le pi/6 and the co-ordinate axes ?

The co-ordinates of the point of the curve y=x-(4)/(x) , where the tangent is parallel to the line y=2x is