Question:

The area bounded by the parabola $ {{y}^{2}}=8x $ and its latus rectum in sq unit is

Updated On: Jun 7, 2024
  • $16/3 \, sq unit$
  • $32/3 \, sq unit$
  • $8/3 \, sq unit$
  • $64/3\, sq unit$
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The Correct Option is B

Solution and Explanation

The given equation of parabola is
$ {{y}^{2}}=8x $ ...(i)
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Concepts Used:

Area under Simple Curves

  • The area of the region bounded by the curve y = f (x), x-axis and the lines x = a and x = b (b > a) - given by the formula:
\[\text{Area}=\int_a^bydx=\int_a^bf(x)dx\]
  • The area of the region bounded by the curve x = φ (y), y-axis and the lines y = c, y = d - given by the formula:
\[\text{Area}=\int_c^dxdy=\int_c^d\phi(y)dy\]

Read More: Area under the curve formula