A farmer has a piece of land. He wishes to divide equally in his three sons to maintain peace and harmony in the family. His land is denoted by area bounded by x = 0, x = 4, y = 4, and y = 0. Find whether he would be able to divide the area equally if he draws the curves y²= 4x and x²= 4y. What is the importance of equality among the people?
The point of intersection of the
Parabolas y2 = 4x and x2 = 4y are (0, 0) and (4, 4)
Now, the area of the region OAQBO bounded by curves y2 = 4x and x2 = 4y
(i)
Again, the area of the region OPQAO bounded by the curves x2 = 4y, x = 0, x = 4andx-axis
(ii)
Similarly, the area of the region OBQRO bounded by the curve y2 = 4x, y-axis,
y = 0 and y = 4
(iii)
From (i) (ii),(iii)it is concluded that the area of the region OAQBO = area of the region OPQAO = area of the region OBQRO, i.e., area bounded by parabolas y2 = 4x and x2 = 4y divides the area of the square in three equal parts.
Hence, the farmer will be able to divide the land equally among his three sons.
Equality helps to maintain peace and harmony in all aspect of society.
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