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Question
Find the area of the region bounded by the parabola y2 = 16x and its latus rectum.
Solution
Comparing y2 = 16x with y2 = 4ax, we get
4a = 16
∴ a = 4
∴ Focus is S(a, 0) = (4, 0)
For y2 = 16x, y = `4sqrt(x)`
Required area = area of the region OBSAO
= 2[area of the region OSAO]
= `2int_0^4 y*dx`, where y = `4sqrt(x)`
= `2int_0^4 4sqrt(x)*dx`
= `8[(x^(3/2))/(3/2)]_0^4`
= `8[2/3(4)^(3/2) - 0]`
= `8[2/3(2^2)^(3/2)]`
= `(128)/(3)` sq. units
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