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.

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.

The area bounded by the coordinate axes and the curve sqrt(x) + sqrt(y) = 1 , is

Find the coordinates of the point on the curve y^2=3-4x where tangent is parallel to the line 2x+y-2=0 .

The area (in sq. units) bounded by the curve |y|=|ln|x|| and the coordinate axes is

If the tangent line at a point (x ,\ y) on the curve y=f(x) is parallel to y-axis, find the value of (dx)/(dy) .

The curve y=ax^2+bx +c passes through the point (1,2) and its tangent at origin is the line y=x . The area bounded by the curve, the ordinate of the curve at minima and the tangent line is

If the curve y=ax^(2)+bx+c passes through the point (1, 2) and the line y = x touches it at the origin, then

The area enclosed between the curve y = log_e (x +e ) and the coordinate axes is

Find the eqution of the curve passing through the point (1,1), if the tangent drawn at any point P(x,y) on the curve meets the coordinate axes at A and B such that P is the mid point of AB.

Find the equation of the curve passing through the point (0, -2) given that at any point (x , y) on the curve the product of the slope of its tangent and y coordinate of the point is equal to the x-coordinate of the point.