AP EAMCET · Maths · Pair of Lines
If the pair of lines \(a x^2-7 x y-3 y^2=0\) and \(2 x^2+x y-6 y^2=0\) have exactly one line in common and ' \(a\) ' is an integer, then the equation of the pair of bisectors of the angles between the lines \(a x^2-7 x y-3 y^2=0\) is
- A \(7 x^2+18 x y-7 y^2=0\)
- B \(x^2-16 x y-y^2=0\)
- C \(7 x^2-9 x y-7 y^2=0\)
- D \(x^2-8 x y-y^2=0\)
Answer & Solution
Correct Answer
(A) \(7 x^2+18 x y-7 y^2=0\)
Step-by-step Solution
Detailed explanation
\(2 x^2+x y-6 y^2=0 \implies 2 + m - 6 m^2 = 0 \implies (3m-2)(2m+1)=0 \) \(m = 2/3\) or \(m = -1/2\) \(a x^2-7 x y-3 y^2=0 \implies a - 7m - 3m^2 = 0 \) For common line, choose integer 'a': If \(m = 2/3\):…
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