COMEDK · Maths · 11. Pair of Lines
Let the equation of pair of lines \(y=m_1 x\) and \(y=m_2 x\) can be written as \(\left(y-m_1 x\right)\left(y-m_2 x\right)=0\). Then, the equation of the pair of the angle bisector of the line \(3 y^2-5 x y-2 x^2=0\) is
- A \(x^2-2 x y+y^2=0\)
- B \(x^2 - 2xy - y^2 = 0\)
- C \(x^2-x y+y^2=0\)
- D \(x^2+5 x y-y^2=0\)
Answer & Solution
Correct Answer
(B) \(x^2 - 2xy - y^2 = 0\)
Step-by-step Solution
Detailed explanation
Rewriting \(3y^2 - 5xy - 2x^2 = 0\) as \(-2x^2 - 5xy + 3y^2 = 0\) Comparing with \(ax^2 + 2hxy + by^2 = 0\): \(a = -2, \quad 2h = -5 \Rightarrow h = -\dfrac{5}{2}, \quad b = 3\) Using the angle bisector formula \(\dfrac{x^2 - y^2}{a - b} = \dfrac{xy}{h}\):…
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