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Question: Answered & Verified by Expert
The lines \(a x^2+2 h x y+b y^2=0\) are at right angles if
MathematicsPair of LinesAP EAMCETAP EAMCET 2020 (18 Sep Shift 1)
Options:
  • A \(a+b=0\)
  • B \(a+b=1\)
  • C \(h^2-a b=0\)
  • D \(a=b\)
Solution:
1903 Upvotes Verified Answer
The correct answer is: \(a+b=0\)
The acute angle \((\theta)\) between lines represented by equation \(a x^2+2 h x y+b y^2=0\), is
\(\theta=\tan ^{-1}\left(\frac{2 \sqrt{h^2-a b}}{|a+b|}\right)\)
If lines are perpendicular then \(a+b=0\).

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