A variable line with negative slope is drawn through the fixed point A(3,4). If it cuts the coordinate axes at B and C, find the minimum value of the area of ΔBCG, where G is the centroid of the ΔOBC. (O is origin)
A
8
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B
10
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C
12
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D
6
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Solution
The correct option is A8 Let slope of line =−tanθ Area of ΔBGC =13 area of ΔOBC =16(3+4cotθ)(4+3tanθ) =16(24+16cotθ+9tanθ) 16cotθ+9tanθ2≥√16×9=12 ∴ Minimum area of ΔBCG=16(24+24)=8