AP EAMCET · Maths · Straight Lines
If one of the lines given by the equation \(2 x^2+a x y+3 y^2=0\) coincide with one of those given by the equation \(2 x^2+b x y-3 y^2=0\), while the other two lines are perpendicular to each other, then the values of \(a\) and \(b\) are
- A \(a=-5\) and \(b=1\)
- B \(a=-4\) and \(b=-1\)
- C \(a=4\) and \(b=1\)
- D \(a=-5\) and \(b=-1\)
Answer & Solution
Correct Answer
(D) \(a=-5\) and \(b=-1\)
Step-by-step Solution
Detailed explanation
Given, equation of pair of straight line \(2 x^2+a x y+3 y^2=0\) and \(2 x^2+b x y-3 y^2=0\) Let the slope of line \(m\) and \(m_1\) of the equation \(2 x^2+a x y+3 y^2=0\) \(\therefore \quad m+m_1=\frac{-a}{3}\) and \(m m_1=\frac{2}{3}\) Slope of the other line is \(m\) and…
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