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

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We are given the curve $ x^2 + y^2 + xy + x + 3y + 1 = 0 $ and the line $ x + y + 2 = 0 $. To find the combined equation of the bisectors of the angles formed by the lines joining the origin to the points of intersection of the curve and the line, we first find the points of intersection. Substitute $ y = -x - 2 $ into the equation of the curve and solve for $ x $. Once the points of intersection are found, we can use the standard formula for the combined equation of angle bisectors for two lines. After solving the equations, we arrive at the equation $ x^2 + 4xy - y^2 = 0 $, which represents the combined equation of the bisectors.

Answer

$ x^2 + 4xy - y^2 = 0 $

Answer

$ x^2 - 4xy + y^2 = 0 $

Answer

$ 2x^2 - 3xy + y^2 = 0 $

Answer

$ x^2 + 2xy - 3y^2 = 0 $

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

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