VITEEE 2010 Paper

Let both of the ends of the rod are on x - axis and y - axis. Let AB be rod of length l and coordinates of A and B be (a,0) and (0,b) respectively.
Let P(h,k) be the mid point of the rod AB.
Then, [

h= 0+a 2 = a 2

k= b+0 2 = b 2

]...(i)
In Δ OAB,
OA2+OB2=AB2
⇒ a2+b2=l2
⇒ (2h)2+(2k)2=l2‌‌‌‌[using‌eq.(i)]
⇒ h2+k2=

l2

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∴ The equation of locus is
x2+y2=

l2

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