Question

Sol. [Key Concept: Bisector of the angle containing a point: take $\frac{a_{1}x + b_{1}y + c_{1}}{\sqrt{a_{1}^{2 +}b_{1}^{2}}} = \pm \frac{a_{2}x + b_{2}y + c_{2}}{\sqrt{a_{2}^{2 +}b_{2}^{2}}}$, sign fixed by the point.]

$$\because\lbrack 3( - 1) - 4(4) + 12\rbrack\lbrack 12( - 1) - 5(4) + 7\rbrack > 0 $$⇒ Equation of bisector containing ( $- 1,4$ ) in its region is

$$\begin{matrix} & \frac{3x - 4y + 12}{5} = \frac{12x - 5y + 7}{13} \\ & \ + 27y - 121 = 0 \end{matrix}$$