TS EAMCET · Maths · Pair of Lines
If \(\alpha x^2+2 \gamma x y+\beta y^2=0\) is the equation of pair of lines passing through the origin and perpendicular to the pair of lines \(b h x^2+a b x y+a h y^2=0(\mathrm{a} \neq 0, \mathrm{~b} \neq 0)\), then \(\frac{\alpha \beta}{\gamma^2}=\)
- A \(\frac{h^2}{a b}\)
- B \(\frac{-2 h^2}{a b}\)
- C \(\frac{-h^2}{a b}\)
- D \(\frac{4 h^2}{a b}\)
Answer & Solution
Correct Answer
(D) \(\frac{4 h^2}{a b}\)
Step-by-step Solution
Detailed explanation
Given lines: \(b h x^2+a b x y+a h y^2=0\) Equation of perpendicular pair of lines: \(a h x^2 - a b x y + b h y^2 = 0\) Comparing with \(\alpha x^2+2 \gamma x y+\beta y^2=0\): \(\alpha = ah\) \(2 \gamma = -ab \implies \gamma = -\frac{ab}{2}\) \(\beta = bh\)…
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