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AP EAMCET · Maths · Three Dimensional Geometry

A line L passing through the point \((2,0)\) makes an angle \(60^{\circ}\) with the line \(2 x-y+3=0\). If L makes an acute angle with the positive X -axis in the anticlockwise direction. then the Y -intercept of the line L is

  1. A \(\frac{10 \sqrt{3}-16}{11}\)
  2. B \(\frac{3 \sqrt{2}}{\sqrt{7}}\)
  3. C \(\frac{16-10 \sqrt{3}}{11}\)
  4. D \(2\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{16-10 \sqrt{3}}{11}\)

Step-by-step Solution

Detailed explanation

Equation of line passing through the point \((2,0)\) and makes angle \(60^{\circ}\) with \(2 x-y+3=0\) is \(y-y_1=\frac{m \pm \tan \alpha}{1 \mp m \tan \alpha}\left(x-x_1\right) \Rightarrow y=\frac{2 \pm \sqrt{3}}{1 \mp 2 \sqrt{3}}(x-2)\) As line makes acute angle with positive…