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Question

The maximum area of a rectangle inscribed in the circle (x+1)2+(y3)2=64 is

A
64 sq. units
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B
72 sq. units
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C
128 sq. units
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D
8 sq. units
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Solution

The correct option is C 128 sq. units
Area of rectangle ABCD=AB×BC
=2 OP×2 PB
=2rsinθ×2rcosθ, θ<π2
=2r2sin2θ=128sin2θ=A (say)
dAdθ=256cos2θ
Put cos2θ=0θ=π4
Now, d2Adθθ=π/4=512<0
A attains maximum value at θ=π4.
Maximum Area =128×sin(2π4)=128


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