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A line passes through the point (1, 2) and makes $60^{0}$ angle with X-axis. A point on this line at a distance 3 from the point (1, 2) is

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$(\frac{1}{2}, 2 + \frac{3 \sqrt{3}}{2})$

$(\frac{3}{2}, 2 + \frac{\sqrt{3}}{2})$

$(\frac{- 5}{2}, 2 - \frac{3 \sqrt{3}}{2})$

$(\frac{5}{2}, 2 + \frac{3 \sqrt{3}}{2})$

answer is C.

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Detailed Solution

$(x_{1} + r \cos θ, y_{1} + r \sin θ)$
$= (1 + 3 c o s 60^{o}, 2 + 3 s i n 60^{o}) = (1 + \frac{3}{2}, 2 + \frac{3 \sqrt{3}}{2}) = (\frac{5}{2}, 2 + \frac{3 \sqrt{3}}{2})$

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