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The line 2x - y + 1 = 0 is a tangent to the hyperbola x²/a² - y²/16 = 1. Using the value of a found from this condition, which of the following sets of three numbers CANNOT be the sides of a right-angled triangle?
- 2a, 4, 1
- 2a, 8, 1
- a, 4, 1
- a, 4, 2
Correct answer: 2a, 8, 1
Solution
Tangency gives a² = 17/4, so 2a = sqrt(17); (2a,4,1) satisfies 17 = 16+1, but (2a,8,1) gives 64 vs 18, so it cannot be a right triangle.
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