If the line y=√(3).x cuts the curve x^₃+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).