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AP EAMCET · Maths · Pair of Lines

If \(\frac{x^2}{a}+\frac{2 x y}{h}+\frac{y^2}{b}=0\) represents a pair of straight lines such that the slope of one of the lines is twice the other, then \(\frac{a b}{h^2}=\)

  1. A \(\frac{9}{8}\)
  2. B \(\frac{8}{9}\)
  3. C \(\frac{2 \sqrt{2}}{3}\)
  4. D \(\frac{3}{2 \sqrt{2}}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{9}{8}\)

Step-by-step Solution

Detailed explanation

Let the slopes of the lines be \(m_1\) and \(m_2\). From the equation \(\frac{x^2}{a}+\frac{2 x y}{h}+\frac{y^2}{b}=0\): \(m_1 + m_2 = -\frac{2/h}{1/b} = -\frac{2b}{h}\) \(m_1 m_2 = \frac{1/a}{1/b} = \frac{b}{a}\) Given \(m_2 = 2m_1\):…