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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 \(\tan \theta+\cot \theta=\)

  1. A \(\frac{25}{12}\)
  2. B \(\frac{625}{168}\)
  3. C \(\frac{169}{60}\)
  4. D \(\frac{1681}{360}\)
Verified Solution

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,…