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Q.

The equation of the bisectors of the angles between the lines joining the origin to the points of intersection of the curve x2 + xy + y2 + x + 3y + 1 = 0 and the line x + y + 2 = 0 is

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a

x2 + 4xy - y2 = 0

b

2x2 + 5xy - y2 = 0

c

x2 + 6xy - 2y2 = 0

d

2x2 - 4xy + 2y2 = 0

answer is A.

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Detailed Solution

x2 + xy + y2 + x + 3y + 1 = 0 → (1)
x + y + 2 = 0
x+y2=1(2)
Homogenising (1) with help of (2)
3x2 - y2 - 2xy = 0
Equation of bisector is
x2 + 4xy - y2 = 0

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