Q. 103.8( 73 Votes )
Find the area bounded by the curve x2 = 4y and the line x = 4y – 2.
Answer :
It is given that the area of the region bounded by the parabola x2 = 4y and x = 4y - 2.
Let A and B be the points of intersection of the line and parabola.
Let us calculate the point of intersection of both the curves,
Given: x2 = 4y and x = 4y - 2
Therefore, putting the value of x, equation of parabola, we get,
(4y - 2)2 = 4y
16y2 + 4 - 16y = 4y
16y2 - 20y + 4 = 0'
4y2 - 5y + 1 = 0
4y2 - 4y - y + 1 = 0
4y(y - 1) - 1(y - 1) = 0
y = 1 or y = 1/4
Corresponding values of x are, x = 2 or x = -1
Therefore,
Coordinates of point A are 
Coordinates of point B are (2, 1).
Now, draw AL and BM perpendicular to x axis.
We can see that,
Area OBCA = Area of line - Area of Parabola …(1)
Hence, the area bounded by the x2 = 4y and the line x = 4y – 2 is 
square units.
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