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Find the area of the region common to the parabolas 4y2 = 9x and 3 x2 =16y.
The given equations are,
4y2 = 9x
And 3x2 = 16y.
Equating equation (i) and (ii)
Or
Or x = 4
When we put x = 4 in equation (i) then y = 3,
When we put x = 0 in equation (i) then y = 0,
On solving these two equations, we get the point of intersections.
The points are O (0, 0) and A(4,3). These are shown in the graph below
Now the bounded area is the required area to be calculated, Hence,
Bounded Area, A = [Area between the curve (i) and x axis from 0 to 4] - [Area between the curve (ii) and x axis from 0 to 4]
On integrating the above definite integration,
The required area =
Area of the region common to the parabolas 4y2 = 9x and 3 x2 = 16y is 4 sq. units