Published by:
CGP EDU Academic Team
Published on: August 14, 2026
If the line y = 
x cuts the curve x 3 + y 3 + 3xy + 5x 2 + 3y 2 + 4x + 5y – 1 = 0 at the points A, B, C, then OA · OB · OC is equal to-
A
(3 
– 1)
B
C
2 + 
D
+ 
Text Solution
Verified by ExpertsThe correct answer is:
A
The abscissa of the intersection points of the given line and the given curve is given by the equation
(3 
+ 1)x 3 + (3 
+ 14)x 2 + (5 
+ 4) x – 1 = 0
If x 1 , x 2 , x 3 be the roots of the above equation, then
A ≡ (x 1 , 
x 1 ), B ≡ (x 2 , 
x 2 ) and C ≡ (x 3 , 
x 3 )
Hence, we have
OA · OB · OC = 2x 1 · 2x 2 · 2x 3 = 8x 1 x 2 x 3
= 8 × 
= 8 × 
= 
(3 
– 1).
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