Question bank/JEE Main/Mathematics

The sides of a triangle have the combined equation x^2 - 3y^2
- 2xy + 8y - 4 = 0. The third side, which is variable always passes
through the point (-5, -1). If complete set of values of slope of
third line so that the origin is an interior point of the triangle is
(a, b) then find (b - 10a).
(1)

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[IMAGE] The lines are x - 3y + 2 = 0 and x + y - 2 = 0
Since (-5, -1) lies on x - 3y + 2 = 0, therefore slope of third line
lie in the interval $\left( - 1,\frac{1}{5} \right)$

Source: Grass-G / M-11 Mathematics Paper-2 1Nov.docx