The equation of the line which is 10 units from the origin and normal ray from the origin to it makes an angle $\frac{π}{4}$ with positive direction of x-axis measured in the clock direction is

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

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

$x + y = 20$

$x + y = 10$

answer is C.

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Detailed Solution

Given $α = \frac{- π}{4}, p = 10$

Then the equation of line in normal form is $x \cos α + y \sin α = p$

$\begin{array}{l} \Rightarrow x \cos (\frac{- π}{4}) + y \sin (\frac{- π}{4}) = 10 \\ \Rightarrow x (\frac{1}{\sqrt{2}}) - y (\frac{1}{\sqrt{2}}) = 10 \\ \Rightarrow x - y = 10 \sqrt{2} \end{array}$

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