AP EAMCET · Maths · Pair of Lines
If \(a d \neq 0\) and two of the lines represented by \(a x^3+3 b x^2 y\) \(+3 \mathrm{cxy}^2+\mathrm{dy}^3=0\) are perpendicular, then
- A \(a^2+a c+b d+d^2=0\)
- B \(a^2+3 a c+3 b d+d^2=0\)
- C \(a^2-3 a c-3 b d+d^2=0\)
- D \(a^2+3 a c-3 b d+d^2=0\)
Answer & Solution
Correct Answer
(B) \(a^2+3 a c+3 b d+d^2=0\)
Step-by-step Solution
Detailed explanation
\(a x^3+3 b x^2 y+3 c x y^2+d y^3=0...(i)\) is a homogeneous equation of third degree is \(x \& y\). Let the slopes of the lines be \(m_1, m_2, m_3\). Then, \(m_1, m_2\) and \(m_3\) are the roots of \(\mathrm{dm}^3+3 \mathrm{~cm}^2+3 \mathrm{bm}+a=0 ...(ii)\) Product of roots…
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