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Q.

A stralght line passing through P(3,1)meets the coordinate axes at A and B. It is given that the distance of this straight line from the origin O is maximum. The area of triangle OAB is equal to

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a

503 sq.units

b

253 sq.units

c

203 sq.units

d

1003 sq.units

answer is A.

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Detailed Solution

Line AB will be the farthest from the origin if OP is right angled to the line drawn. OP=10Also, tanθ=13OA=OPsecθ=10×103=103OB=OP cosecθ=10×101=10∴Area of ΔOAB=12(103)(10)=503

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