TS EAMCET · Maths · Straight Lines
If \(\alpha\) and \(\beta\) are the angles made by the normals drawn from the origin to the lines \(x+y+\sqrt{2}=0\) and \(x-\sqrt{3} y-2=0\) with the positive direction of the \(X\)-axis respectively measured in anti-clockwise direction, the \(\alpha+\beta=\)
- A \(-\frac{13 \pi}{12}\)
- B \(\frac{29 \pi}{12}\)
- C \(-\frac{11 \pi}{12}\)
- D \(\frac{35 \pi}{12}\)
Answer & Solution
Correct Answer
(D) \(\frac{35 \pi}{12}\)
Step-by-step Solution
Detailed explanation
Normal drawn from origin to lines \(x+y+\sqrt{2}=0\) and \(x-\sqrt{3} y-2=0\) Equation as normal \(x-y=0\) and \(\sqrt{3} x+y=0\) \[ \alpha=1, \beta=-\frac{1}{\sqrt{3}} \] So, in anticlockisise direction \[ \tan \alpha=-1 \text { and } \tan \beta=\frac{1}{\sqrt{3}} \] So,…
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