The Tangent To The Angle Between The Lines Joining The Origin To The Points Of Intersection Of The Line Y = 3x + 2 And The Curve x2 + 2xy + 3y2 + 4x + 8y – 11 = 0, Is

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Question

The tangent to the angle between the lines joining the origin to the points of intersection of the line y = 3x + 2 and the curve x² + 2xy + 3y² + 4x + 8y – 11 = 0, is

diffcult

Solution

Correct option is

The equation of the given straight line is

He equation of the given curve is

The combined equation of the straight lines joining the origin to the points of intersection of (i) and (ii) is a homogeneous equation of second degree obtained with the help of (i) and (ii). Making the equation (ii) homogenous of the second degree in x and y with the help of (i), we get