JEE Mains · Maths · STD 11 - 9. straight line
The portion of the line \(4 x+5 y=20\) in the first quadrant is trisected by the lines \(\mathrm{L}_1\) and \(\mathrm{L}_2\) passing through the origin. The tangent of an angle between the lines \(\mathrm{L}_1\) and \(\mathrm{L}_2\) is:
- A \(\frac{8}{5}\)
- B \(\frac{25}{41}\)
- C \(\frac{2}{5}\)
- D \(\frac{30}{41}\)
Answer & Solution
Correct Answer
(D) \(\frac{30}{41}\)
Step-by-step Solution
Detailed explanation
Co-ordinates of \(A=\left(\frac{5}{3}, \frac{8}{3}\right)\) Co-ordinates of \(\mathrm{B}=\left(\frac{10}{3}, \frac{4}{3}\right)\) Slope of \(O A=m_1=\frac{8}{5}\) Slope of \(O B=m_2=\frac{2}{5}\) \(\tan \theta=\left|\frac{m_1-m_2}{1+m_1 m_2}\right| \)…
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