AP EAMCET · Maths · Pair of Lines
The equation of the pair of lines passing through the origin whose sum and product of slopes are respectively the arithmetic mean and geometric mean of 4 and 9 is
- A \(12 x^2-13 x y+2 y^2=0\)
- B \(12 x^2+13 x y+2 y^2=0\)
- C \(12 x^2-15 x y+2 y^2=0\)
- D \(12 x^2+15 x y-2 y^2=0\)
Answer & Solution
Correct Answer
(A) \(12 x^2-13 x y+2 y^2=0\)
Step-by-step Solution
Detailed explanation
Let \(m_1\) and \(m_2\) be the slopes of lines. Then, \(m_1+m_2=\) arithmetic mean \(=\frac{13}{2}\) and \(\quad m_1 m_2=\) geometric mean \(=\sqrt{36}=6\). Now, equation of the pair of lines passing through the origin is \[ \left(y-m_1 x\right)\left(y-m_2 x\right)=0 \]…
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