Question

A line makes an angle ${45}^o$ with $X-axis$ and at a distance of $\sqrt{2}$ from the origin. Its equation is

• A. $x+y\sqrt{2}=1$
• B. $\sqrt{2}x+y=1$
• C. $y-x=2$
• D. $y-x=\sqrt{2}$

Answer 1

Answer: (D)

$y-x=\sqrt{2}$

$y-y_1=\tan {45}^0\left(x-x_1\right)$

$y-y_1=x-x_1$

$y-x=\left(y_1-x_1\right)=0$

$y-x=\left(y_1-x_1\right)$

distance from origin=$\frac{\left|y_1-x\right|}{\sqrt{1+}}=\sqrt{2}$

$y_1-x_1=\sqrt{2}$

$Soeqoflineis$

$y-x-\left(\sqrt{2}\right)=0$

$y-x=\sqrt{2}$