What Is the Shortest Possible Length of the Line Segment $y=\frac{5}{x}$

question 123

Multiple Choice

What is the shortest possible length of the line segment that is cut off by the first quadrant and is tangent to the curve $y=\frac{5}{x}$ at some point?

• A) \(\frac{\sqrt{2}}{5}\)
• B) \(\sqrt{2}\)
• C) \(\frac{1}{5}\)
• D) None of these
• E) \(2 \sqrt{10}\)

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