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
- A \(\frac{10 \sqrt{3}-16}{11}\)
- B \(\frac{3 \sqrt{2}}{\sqrt{7}}\)
- C \(\frac{16-10 \sqrt{3}}{11}\)
- D \(2\)
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…
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