AP EAMCET · Maths · Straight Lines
A line \(L\) passes through the point \(P(1,2)\) and makes an angle of \(60^{\circ}\) with \(\overrightarrow{O X}\) in the positive direction. \(A\) and \(B\) are two points lying on \(L\) at a distance of 4 units from P. If 0 is the origin, then the area of \(\triangle 0 \mathrm{AB}\) is
- A \(4-2 \sqrt{3}\)
- B \(8-4 \sqrt{3}\)
- C \(4+2 \sqrt{3}\)
- D \(8+4 \sqrt{3}\)
Answer & Solution
Correct Answer
(A) \(4-2 \sqrt{3}\)
Step-by-step Solution
Detailed explanation
Slope of line \(L\): \(m = \tan(60^{\circ}) = \sqrt{3}\) Equation of line \(L\) through \(P(1,2)\): \(y - 2 = \sqrt{3}(x - 1) \implies \sqrt{3}x - y + (2 - \sqrt{3}) = 0\) Length of base \(AB\): \(AB = 4 + 4 = 8\) Perpendicular distance from origin \(O(0,0)\) to line \(L\):…
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