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The curves x²/α + y²/4 = 1 and y³ = 16x meet orthogonally. Then one possible value of α is:
- 2
- 4/3
- 1/2
- 3/4
Correct answer: 4/3
Solution
The curves meet orthogonally when the product of their slopes at the intersection points equals -1. By calculating the derivatives of both curves and setting up the condition for orthogonality, we find that α must equal 4/3 to satisfy this relationship.
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