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If the line y=√(3).x cuts the curve x3+y3+3xy+5x2+3y2+4x+5y-1=0 at the points A,B,C then OA.OB.OC is
a.{4(3√3-1)}/13
b.3√3+1
c.(2/√3) +7
d.none of these
Hi Menka,
Sub y=root(3)x in the eqn, and form a cubic in x for which say x1,x2,x3 are the roots.
Now OA = √(x1^2 + y1^2) = 2x1 -------- (as y1=root(3)x1)
So OA.OB.OC = 8x1x2x3.....
From the cubic in x, find x1x2x3 using product of roots, and you'll get the value of OA.OB.OC from 8x1x2x3.
Regards,
Ashwin (IIT Madras).
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