Q.

The line xa+yb=1 meets the x -axis at A and y -axis at B and the line y=x at C such that the area of the △AOC is  twice the area of ΔBOC . Then the coordinates of C are

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a

b3,b3

b

2a3,2a3

c

2b3,2b3

d

None of these

answer is C.

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Detailed Solution

Given ΔAOC=2ΔBOC⇒ 12(OA)x1=2×12(OB)x1⇒ a=2b Equation of AB⇒xa+yb=1----(1)x2b+yb=1----(2)⇒ Since point C lies on the line (2)⇒ x12b+x1b=1⇒ x1=2b3=a3⇒C=2b3,2b3
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