TS EAMCET · Maths · Straight Lines
If \(\quad a x^2+2 h x y+b y^2+2 g x+2 f y+c=0\) represents a pair of parallel lines, then \(\sqrt{\frac{g^2-a c}{f^2-b c}}\), is equal to
- A \(\frac{a}{b}\)
- B \(\sqrt{\frac{a}{b}}\)
- C \(\sqrt{\frac{b}{a}}\)
- D \(\frac{b}{a}\)
Answer & Solution
Correct Answer
(B) \(\sqrt{\frac{a}{b}}\)
Step-by-step Solution
Detailed explanation
If \(a x^2+2 h x y+b y^2+2 g x+2 f y+c=0\) represents a pair of parallel lines, then \(\sqrt{\frac{g^2-a c}{a(a+b)}}=\sqrt{\frac{f^2-b c}{b(a+b)}}\) \(\Rightarrow \quad \sqrt{\frac{g^2-a c}{f^2-b c}}=\sqrt{\frac{a}{b}}\)
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