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 \(\frac{a b}{h^2}=\)
- A \(\frac{9}{8}\)
- B \(\frac{8}{9}\)
- C \(\frac{2 \sqrt{2}}{3}\)
- D \(\frac{3}{2 \sqrt{2}}\)
Answer & Solution
Correct Answer
(A) \(\frac{9}{8}\)
Step-by-step Solution
Detailed explanation
Let the slopes of the lines be \( m \) and \( 2m \). The equation \( \frac{x^2}{a}+\frac{2 x y}{h}+\frac{y^2}{b}=0 \) can be written as a quadratic in slope \( \left(m = \frac{y}{x}\right) \): \( \frac{1}{b} m^2 + \frac{2}{h} m + \frac{1}{a} = 0 \)…
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