In cartesian coordinate system we take the x-y plane a d draw the line x=y in 1st quadrant now we can say that this line divides the plane of 1st quadrant into two equal halves which means area under this line will represent half of the area and 1/8th of area of plane
On integrating to find area under the curve we get Area of half plane as x^2/2 x being positive which means the total area of a plane has to be ×8 of this area I.e 4x^2 which represents equation of a parabola .
Conclusion: area of the plane is represented by parabolic equation . Is there any logic behind it or did I do something wrong