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Question

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 A 8
Let slope of line =tanθ
Area of ΔBGC
=13 area of ΔOBC
=16(3+4cotθ)(4+3tanθ)
=16(24+16cotθ+9tanθ)
16cotθ+9tanθ216×9=12
Minimum area of ΔBCG=16(24+24)=8
111155_76648_ans.jpg

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