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) passes through the origin. Through any point (x,y) on the curve, lines are drawn parallel to the coordinate axes. If the curve divides the area formed by these lines and coordinates 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

Through any point (x,y) of a curve which passes through the origin, lines are drawn parallel to the coordinate axes. Given that it divides the rectangle formed by the two lines and the axes into two areas one of which is twice the other, show that such a curve is parabola.

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

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

A curve passes through the poit (5,3) and at any point (x,y) on it the product of its slope and the ordinate is equal to abscissa of the curve is

The finite area of the region formed by co-ordinate axes and the curve y=log_(e)x is

The finite area of the region formed by co-ordinate axes and the curve y=log_(e)x is