Which of the following is/are correct with respect to angle bisectors of pair of lines $3 x^{2} - 4 y^{2} - x y - 12 x + 16 y = 0$

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Equation of acute angle bisector is $(3 \sqrt{2} + 5) x - (4 \sqrt{2} - 5) y - 20 = 0$

Angle bisector containing point $(2, 1)$ is the obtuse angle bisector

Angle bisectors are perpendicular to each other

Equation of obtuse angle bisector is $(3 \sqrt{2} + 5) x - (4 \sqrt{2} - 5) y - 20 = 0$

answer is A, C, D.

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Detailed Solution

Bisectors are given by $\frac{3 x - 4 y}{5} = \pm (\frac{x + y - 4}{\sqrt{2}}) .$ Bisector containing $(2, 1)$ is given by ‘-’ sign which is also obtuse angle bisector

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