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  •  If the line cuts the curve <img alt="\mathrm{x^{3}+y^{2}+3 x^{2

 If the line \mathrm{y=\sqrt{3} x} cuts the curve \mathrm{x^{3}+y^{2}+3 x^{2}+8=0} at the points A, B, C, then OA.OB.OC ( O being origin) equals

Option: 1

-32


Option: 2

-64


Option: 3

108


Option: 4

-100


Answers (1)

best_answer

Parametric equation of line

\mathrm{y=\sqrt{3} x \text { is } \frac{x}{\frac{1}{2}}=\frac{y}{\frac{\sqrt{3}}{2}}=r}

Any point on this line \mathrm{\left(\frac{r}{2}, \frac{\sqrt{3} r}{2}\right)}
At point of intersection this point will also satisfy \mathrm{x^{3}+y^{2}+3 x^{2}+8=0}
\mathrm{ \Rightarrow \frac{r^{3}}{8}+\frac{3 r^{2}}{4}+\frac{3 r^{2}}{4}+8=0}
\mathrm{ \Rightarrow r^{3}+12 r^{2}+64=0}
\mathrm{ \Rightarrow \text { OA.OB.OC }=-64 }

Hence (B) is the correct answer.

 

Posted by

SANGALDEEP SINGH

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