Straight Line And Pair Of Straight Lines Ques 78

Answer:

Correct Answer: 78.$(4+\sqrt{5}) x-(2 \sqrt{5}+3) y+(4 \sqrt{5}+2)=0$

Solution:

78. Given equations of lines are

$x-2 y+4=0$ and $4 x-3 y+2=0$

Here, $\quad a _1 a _2+b _1 b _2=1(4)+(-2)(-3)=10>0$

For obtuse angle bisector, we take negative sign.

$$ \begin{array}{lc} \therefore & \frac{x-2 y+4}{\sqrt{5}}=-\frac{4 x-3 y+2}{5} \\ \Rightarrow & \sqrt{5}(x-2 y+4)=-(4 x-3 y+2) \\ \Rightarrow & (4+\sqrt{5}) x-(2 \sqrt{5}+3) y+(4 \sqrt{5}+2)=0 \end{array} $$