AP EAMCET · Maths · Straight Lines
The angle made by a line L with positive X - axis measured in the positive direction is \(\frac{\pi}{6}\) and the intercept made by \(L\) on \(Y\) - axis is negative. If \(L\) is at a distance of 5 units from the origin, then the perpendicular distance from the point \((1,-\sqrt{3})\) to the line L is
- A \(2\)
- B \(1\)
- C \(4\)
- D \(3\)
Answer & Solution
Correct Answer
(D) \(3\)
Step-by-step Solution
Detailed explanation
\(m = \tan\left(\frac{\pi}{6}\right) = \frac{1}{\sqrt{3}}\) \(L: y = \frac{1}{\sqrt{3}}x + c \implies x - \sqrt{3}y + \sqrt{3}c = 0\) \(\frac{|\sqrt{3}c|}{\sqrt{1^2 + (-\sqrt{3})^2}} = 5 \implies \frac{|\sqrt{3}c|}{2} = 5 \implies \sqrt{3}c = -10\) (since Y-intercept is…
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