TS EAMCET · Maths · Straight Lines
Angles made with the \(X\)-axis by the two lines passing through the point \(P(1,2)\) and cutting the line \(x+y=4\) at a distance \(\frac{\sqrt{6}}{3}\) units from the point \(P\) are
- A \(\frac{\pi}{5}\) and \(\frac{3 \pi}{10}\)
- B \(\frac{\pi}{6}\) and \(\frac{\pi}{3}\)
- C \(\frac{\pi}{12}\) and \(\frac{5 \pi}{12}\)
- D \(\frac{\pi}{8}\) and \(\frac{3 \pi}{8}\)
Answer & Solution
Correct Answer
(C) \(\frac{\pi}{12}\) and \(\frac{5 \pi}{12}\)
Step-by-step Solution
Detailed explanation
Let slope of line is \(m\) \(\therefore\) Equation of line is \(\begin{aligned} & y-2=m(x-1) \\ & y-2=m x-m \\ & m x-y+(2-m)=0 \end{aligned}\) On solving \(m x-y+(2-m)\) and \(x+y=4\), we get \((x, y)=\left(\frac{m+2}{m+1}, \frac{3 m+2}{m+1}\right)\) Now, it is given that…
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