Question

A rod of fixed length k slides along the coordinate axes. If it meets the axes at A(a,0) and B(0,b), then the minimum value of \((a + \frac 1a)^2 + (b + \frac 1b)^2 \) is

a. 0

b. 8

c. \(k^2 -4+\frac4{k^2}\)

d. \(k^2 +4+\frac4{k^2}\)

Answer 1

Correct option is d. \(k^2 +4+\frac4{k^2}\)