TS EAMCET · Maths · Pair of Lines
A value of \(k\) such that the straight lines \(y-3 k x+4=0\) and \((2 k-1) x-(8 k-1) y\) \(-6=0\) are perpendicular is
- A \(\frac{1}{6}\)
- B \(-\frac{1}{6}\)
- C 1
- D 0
Answer & Solution
Correct Answer
(A) \(\frac{1}{6}\)
Step-by-step Solution
Detailed explanation
Given lines, \[ y-3 k x+4=0 \] \[ \text { and }(2 k-1) x-(8 k-1) y-6=0 \] Slope of Eq. (i), \[ \begin{array}{ll} \text { Slope of Eq. (i), } & m_1=\frac{-(-3 k)}{1}=3 k \\ \text { and slope of Eq. (ii) } & m_2=\frac{-(2 k-1)}{-(8 k-1)}=\frac{2 k-1}{8 k-1} \end{array} \] Since,…
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