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The region enclosed between the parabola y² = 4*lambda*x and the straight line y = lambda*x (with lambda > 0) has an area of 1/9 square units. Find the value of lambda.
- 24
- 12
- 48
- 8
Correct answer: 24
Solution
The enclosed area of y² = 4*lambda*x and y = lambda*x works out to 8/(3*lambda). Setting this equal to 1/9 and solving gives lambda = 24. Because the area is inversely proportional to lambda, a smaller required area forces a larger lambda.
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