TS EAMCET · Maths · Straight Lines
A line L perpendicular to the line \(5 x-12 y+6=0\) makes positive intercept on the Y axis. If the distance from the origin to the line L is 2 units and the angle made by the perpendicular drawn from the origin to the line L with positive X -axis is \(\theta\), then \(\tan \theta+\cot \theta=\)
- A \(\frac{25}{12}\)
- B \(\frac{625}{168}\)
- C \(\frac{169}{60}\)
- D \(\frac{1681}{360}\)
Answer & Solution
Correct Answer
(C) \(\frac{169}{60}\)
Step-by-step Solution
Detailed explanation
\(m_1 = \frac{5}{12}\) \(m_L = -\frac{1}{m_1} = -\frac{12}{5}\) Line L: \(y = -\frac{12}{5}x + c \Rightarrow 12x + 5y - 5c = 0\) \(\frac{|12(0) + 5(0) - 5c|}{\sqrt{12^2 + 5^2}} = 2 \Rightarrow \frac{|-5c|}{13} = 2\) Since L makes positive intercept on Y axis,…
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