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AP EAMCET · Maths · Straight Lines

If \(k_1>k_2\) are the two values of \(\mathrm{k}\) such that the lines \(y-3 k x+4=0\) and \((2 k-1) x-(8 k-1) \mathrm{y}-6=0\) are perpendicular, then the equation of the line passing through \(\left(k_1, k_2\right)\) and having the slope \(\left(\frac{k_2}{k_1}\right)\) is

  1. A \(3 x+2 y=0\)
  2. B \(6 x-2 y=3\)
  3. C \(12 x-5 y=7\)
  4. D \(6 x+y=0\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(6 x+y=0\)

Step-by-step Solution

Detailed explanation

\(m_1 = 3k, m_2 = \frac{2k-1}{8k-1}\) \(m_1 m_2 = -1 \Rightarrow 3k \left(\frac{2k-1}{8k-1}\right) = -1\) \(6k^2 - 3k = -8k + 1\) \(6k^2 + 5k - 1 = 0\) \((6k-1)(k+1) = 0\) \(k = \frac{1}{6}, k = -1\) \(k_1 > k_2 \Rightarrow k_1 = \frac{1}{6}, k_2 = -1\) Point:…