Find the area of the parabola y^2 = 4ax bounded by its latus rectum. - Mathematics MCQ Mathematics Mock Test - 3 2026 | ExamTest.live

mediumMCQMathematics Mock Test - 32026Mathematics

1 mark

Find the area of the parabola y^{2} = 4 a x bounded by its latus rectum.

Solution & Step-by-step Explanation

The latus rectum of y^{2} = 4 a x is the line x = a .The parabola is symmetric about the x-axis. Area = 2 \int_{0}^{a} 4 a x d x = 4 a \int_{0}^{a} x^{1/2} d x Area = 4 a [\frac{x ^{3/2}}{3/2}]_{0}^{a} = 4 a \cdot \frac{2}{3} a^{3/2} Area = \frac{8}{3} a^{1/2 + 3/2} = \frac{8 a ^{2}}{3}

Try it yourself before checking the explanation above.

Find the area of the parabola y^{2} = 4 a x bounded by its latus rectum.

\frac{4 a ^{2}}{3}

\frac{8 a ^{2}}{3}

\frac{10 a ^{2}}{3}

None of these

Practice with timed mock tests and track your performance across Mathematics.