Find the area of the region bounded by the parabola \(y^2 = 16x\) and its latus rectum.
Q.13 Find the area of the region bounded by the parabola \(y^2 = 16x\) and its latus rectum.
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Answer: \(\dfrac{128}{3}\) sq. units
Comparing with \(y^2 = 4ax\): \(4a = 16\), \(a = 4\). The latus rectum is \(x = 4\). The region is symmetric about the X-axis, and \(y = 4\sqrt x\) for the upper half.
Area \(= 2\int_0^4 4\sqrt x\,dx = 8\left[\dfrac{2}{3}x^{3/2}\right]_0^4 = 8\cdot\dfrac23\cdot 8 = \dfrac{128}{3}\) sq. units.
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· 28 Oct 2026
AI-verified · Oct 2026
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