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# If the area bounded by the parabola y^{2} = 16ax and the line y = 4kx is sq unit, then using integration find the value of k.

Answer :

Given; The area bounded by the parabola y^{2} = 16ax and the line y = 4kx is sq unit

By solving the equations;

16k^{2}x^{2} = 16ax

Area of the region bounded by the curve y=f(x), the x-axis and the ordinates x=a and x=b, where f(x) is a continuous function defined on [a,b], is given by .

∴ Require Area

∴ k^{3} = 8

∴ k = 3

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