AP EAMCET · Maths · Pair of Lines
If two of the lines represented by \(2 x^3+x^2 y+y^3=0\) are mutually perpendicular, then the slope of the third line is
- A \(2\)
- B \(1\)
- C \(0\)
- D \(\frac{1}{2}\)
Answer & Solution
Correct Answer
(A) \(2\)
Step-by-step Solution
Detailed explanation
The equation representing the slopes \(m\) is obtained by substituting \(y=mx\) into \(2x^3+x^2y+y^3=0\): \(2x^3+x^2(mx)+(mx)^3=0 \implies 2+m+m^3=0 \implies m^3+m+2=0\) Let the slopes be \(m_1, m_2, m_3\). From Vieta's formulas: \(m_1 m_2 m_3 = -2\) Given that two lines are…
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