Q85 / 160 · AP EAMCET 2024 (22 May Shift 2) · Mathematics
The equation of a line which makes an angle of $45^{\circ}$ with each of the pair of lines $x y-x-y+1=0$ is
- Correct answerA$x-y=5$
- B$2 x+y=3$
- C$x+7 y=8$
- D$3 x-y=2$
Solution
Given pair of lines : $x y-x-y+1=0$
$\Rightarrow x(y-1)-1(y-1)=0 \Rightarrow(x-1)(y-1)=0$
lines are $x-1=0$ and $y-1=0$
Let required line be $y=m x+\mathrm{c}$
Now, angle between $y-1=0$ and $y=m x+c$ is $45^{\circ}$
$\Rightarrow \tan 45^{\circ}=\left|\frac{m-0}{1+0}\right| \Rightarrow m=1$
So, all the lines parallel to $y=x+c$ makes $45^{\circ}$ with the given pair of lines So, according to option $x-y=5$ is correct.
So, all the lines parallel to $y=x+c$ makes $45^{\circ}$ with the given pair of lines So, according to option $x-y=5$ is correct.
Hence, the correct answer is option: 'A'.