TS EAMCET · Maths · Pair of Lines
The numbers \(\alpha\) and \(\beta\) are such that one of the lines of \(2 x^2+\alpha x y+3 y^2=0\). Coincides with one of the lines of \(2 x^2+\beta x y-3 y^2=0\). If the two lines other than that line are perpendicular, then \(|\alpha+\beta|\) is equal to
- A 5
- B 4
- C 0
- D 6
Answer & Solution
Correct Answer
(D) 6
Step-by-step Solution
Detailed explanation
Let \(\frac{2}{3} x^2+\frac{\alpha}{3} x y+y^2=(y-m x)\left(y-m^{\prime} x\right)\) and \(\frac{2^{\mathrm{I}}}{-3} x^2+\frac{\beta}{-3} x y+y^2=\left(y+\frac{1}{m} x\right)\left(y-m^{\prime} x\right)\) Then, \(m+m^{\prime}=-\frac{\alpha}{3}, m m^{\prime}=\frac{2}{3}\)…
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