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AP EAMCET · Maths · Pair of Lines

If the slopes of both the lines given by \(x^2+2 h x y+6 y^2=0\) are positive and the angle between these lines is \(\operatorname{Tan}^{-1}\left(\frac{1}{7}\right)\), then the product of the perpendiculars

  1. A \(\frac{1}{6}\)
  2. B \(\frac{1}{5 \sqrt{2}}\)
  3. C \(\frac{5}{6}\)
  4. D \(\frac{1}{3 \sqrt{2}}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{1}{5 \sqrt{2}}\)

Step-by-step Solution

Detailed explanation

\(A=1, B=6, H=h\) \(\tan\theta = \left|\frac{2\sqrt{H^2-AB}}{A+B}\right| \Rightarrow \frac{1}{7} = \left|\frac{2\sqrt{h^2-6}}{1+6}\right|\) \(1 = 2\sqrt{h^2-6} \Rightarrow h^2 = \frac{25}{4}\)…