COMEDK · Maths · 11. Pair of Lines
Let the equation of the pair of lines \(y=p x\) and \(y=q x\) can be written as \((y-p x)(y-q x)=0\). Then the equation of the pair of the angle bisectors of the line \(x^2-4 x y-5 y^2=0\) is
- A \(x^2-3 x y+y^2=0\)
- B \(x^2+4 x y-y^2=0\)
- C \(x^2+3 x y-y^2=0\)
- D \(x^2-3 x y-y^2=0\)
Answer & Solution
Correct Answer
(C) \(x^2+3 x y-y^2=0\)
Step-by-step Solution
Detailed explanation
The given equation of the pair of lines is \(x^2 - 4xy - 5y^2 = 0\). Comparing this with the general homogeneous equation of the second degree \(ax^2 + 2hxy + by^2 = 0\), we have \(a = 1\), \(2h = -4\) (so \(h = -2\)), and \(b = -5\). The equation of the pair of angle bisectors…
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