TS EAMCET · Maths · Pair of Lines
The number of real values of \(\alpha\) for which the pair of lines represented by \(\left(\alpha^2+12|\alpha|\right) x^2+6 x y+(18-21|\alpha|) y^2=0\) are at right angles to each other, is
- A 0
- B 1
- C 2
- D 4
Answer & Solution
Correct Answer
(D) 4
Step-by-step Solution
Detailed explanation
Condition for right angles: \(A+B=0\) \((\alpha^2 + 12|\alpha|) + (18 - 21|\alpha|) = 0\) \(\alpha^2 - 9|\alpha| + 18 = 0\) Let \(x = |\alpha|\). Then \(x^2 - 9x + 18 = 0\) \((x-3)(x-6) = 0\) \(x=3\) or \(x=6\) \(|\alpha|=3 \implies \alpha = \pm 3\)…
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