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The region bounded by the parabola y² = 4ax and the line y = ax has area 1/3 square unit. For the same parabola, what is the area enclosed by the line y = 4x?
- 8 square units
- 4 square units
- 4/3 square units
- 8/3 square units
Correct answer: 8/3 square units
Solution
Area between y^2=4ax and y=ax is 8/(3a)=1/3, so a=8 and the parabola is y^2=32x. With y=4x: intersection at x=2, area = integral 0->2 (sqrt(32x)-4x) dx = 32/3 - 8 = 8/3 square units.
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