AP EAMCET · Maths · Pair of Lines
For \(a, b, h>0\), if the slope of one of the lines represented by \(a^2 x^2+2 h x y+b^2 y^2=0\) is twice that of the other, then the value of \(\frac{h}{a b}\) is
- A \(\frac{3 \sqrt{2}}{4}\)
- B \(\frac{2 \sqrt{3}}{4}\)
- C \(\frac{-2 \sqrt{3}}{4}\)
- D \(\frac{-3 \sqrt{2}}{4}\)
Answer & Solution
Correct Answer
(A) \(\frac{3 \sqrt{2}}{4}\)
Step-by-step Solution
Detailed explanation
Given, lines are \(a^2 x^2+2 h x y+b^2 y^2=0\) Let \(m\) and \(2 m\) be the slopes of the lines. Then, \(m+2 m=\frac{-2 h}{b^2}\). \(\Rightarrow \quad 3 m=-\frac{2 h}{b^2}\) \(\Rightarrow \quad m=-\frac{2 h}{3 b^2}\)...(i) and \(m \times 2 m=\frac{a^2}{b^2}\)…
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