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The equation of the line which is at 10 units from the origin and the normal from the origin to it makes an angle $\frac{π}{4}$ with the X-axis in the negative direction is

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$x + y + 10 \sqrt{2} = 0$

$x - y - 10 \sqrt{2} = 0$

$x + y - 10 \sqrt{2} = 0$

$x - y + 10 \sqrt{2} = 0$

answer is D.

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Detailed Solution

$xcos (180 - 45) + ysin (180 - 45) = 10$

$\begin{array}{l} \Rightarrow - x \frac{1}{\sqrt{2}} + y \cdot \frac{1}{\sqrt{2}} = 10 \\ \Rightarrow x - y + 10 \sqrt{2} = 0 \end{array}$

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