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AP EAMCET · Maths · Straight Lines

If a straight line is at a distance of 10 units from the origin and the perpendicular drawn from the origin to it makes an angle \(\frac{\pi}{4}\) with the negative X -axis in the negative direction then the equation of that line is

  1. A \(x+y+10 \sqrt{2}=0\)
  2. B \(x-y-10 \sqrt{2}=0\)
  3. C \(\mathrm{x}+\mathrm{y}-10 \sqrt{2}=0\)
  4. D \(x-y+10 \sqrt{2}=0\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(x-y+10 \sqrt{2}=0\)

Step-by-step Solution

Detailed explanation

\( \text{Normal form of the line: } x \cos \alpha + y \sin \alpha = p \) \( p = 10 \) \( \alpha = \pi - \frac{\pi}{4} = \frac{3\pi}{4} \) \( \cos \left(\frac{3\pi}{4}\right) = -\frac{1}{\sqrt{2}} \) \( \sin \left(\frac{3\pi}{4}\right) = \frac{1}{\sqrt{2}} \)…