COMEDK · Maths · 10. Straight Lines
The perpendicular distance of a line from the origin is 5 units and its slope is \(-1\).
The equation of the line is
- A \(x+y \pm 2 \sqrt{5}=0\)
- B \(x-y \pm 5 \sqrt{2}=0\)
- C \(x+y \pm 5 \sqrt{2}=0\)
- D \(x-y \pm 2 \sqrt{5}=0\)
Answer & Solution
Correct Answer
(C) \(x+y \pm 5 \sqrt{2}=0\)
Step-by-step Solution
Detailed explanation
The equation of a line with slope \(m = -1\) can be written in the form \(y = mx + c\), which is \(y = -x + c\) or \(x + y - c = 0\). The perpendicular distance \(d\) of the line \(Ax + By + C = 0\) from the origin \((0, 0)\) is given by \(d = \dfrac{|C|}{\sqrt{A^2 + B^2}}\).…
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