Straight Line and Pair of Straight Lines 2 Question 7
7. Find the equation of the line which bisects the obtuse angle between the lines $x-2 y+4=0$ and $4 x-3 y+2=0$.
(1993, 2M)
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Answer:
Correct Answer: 7. $(4+\sqrt{5}) x-(2 \sqrt{5}+3) y+(4 \sqrt{5}+2)=0$
Solution:
- 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.
$$ \begin{array}{lc} \therefore & \frac{x-2 y+4}{\sqrt{5}}=-\frac{4 x-3 y+2}{5} \\ \Rightarrow & \sqrt{5}(x-2 y+4)=-(4 x-3 y+2) \\ \Rightarrow & (4+\sqrt{5}) x-(2 \sqrt{5}+3) y+(4 \sqrt{5}+2)=0 \end{array} $$
