AP EAMCET · Maths · Pair of Lines
The equation \((2 p-3) x^2+2 p x y-y^2=0\) represents a pair of distinct lines
- A Only when \(p=0\)
- B For all values of \(p \in R-[-3,1]\)
- C For all values of \(p \in(-3,1)\)
- D For all values of \(p \in R\)
Answer & Solution
Correct Answer
(B) For all values of \(p \in R-[-3,1]\)
Step-by-step Solution
Detailed explanation
\(A = 2p-3, B = 2p, C = -1\) \(B^2 - 4AC > 0\) \((2p)^2 - 4(2p-3)(-1) > 0\) \(4p^2 + 8p - 12 > 0\) \(p^2 + 2p - 3 > 0\) \((p+3)(p-1) > 0\) \(p \in (-\infty, -3) \cup (1, \infty)\) \(p \in R-[-3,1]\)
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