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AP EAMCET · Maths · Straight Lines

If the line \((2 x+3 y+4)+\lambda(6 x-y+12)=0\) is perpendicular to the line \(7 x+5 y=2\), then \(\lambda=\)

  1. A \(\frac{-27}{39}\)
  2. B \(\frac{-29}{37}\)
  3. C \(\frac{-27}{37}\)
  4. D \(\frac{-28}{37}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{-29}{37}\)

Step-by-step Solution

Detailed explanation

Slope of first line: \(m_1 = -\frac{2+6\lambda}{3-\lambda}\) Slope of second line: \(m_2 = -\frac{7}{5}\) \(m_1 m_2 = -1 \implies \left(-\frac{2+6\lambda}{3-\lambda}\right) \left(-\frac{7}{5}\right) = -1\) \(7(2+6\lambda) = -5(3-\lambda)\) \(14+42\lambda = -15+5\lambda\)…