Question

Prove that the curves y²= 4 x and x² = 4y divide the area of square bounded by x = 0,=4,y= 0 into three equal parts​

Answer 1

Answer:

Step-by-step explanation:

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 = 4 and x-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.