TS EAMCET · Maths · Pair of Lines
The value of ' \(a\) ' for which the equation \(\left(a^2-3\right) x^2+16 x y-2 a y^2+4 x-8 y-2=0\) represents a pair of perpendicular lines is
- A \(2\)
- B \(-1\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(C) \(3\)
Step-by-step Solution
Detailed explanation
For perpendicular lines, \(A+B=0\). \((a^2-3) + (-2a) = 0 \implies a^2 - 2a - 3 = 0 \implies (a-3)(a+1) = 0\) \(a=3\) or \(a=-1\). For a pair of straight lines, \(\Delta = ABC + 2FGH - AF^2 - BG^2 - CH^2 = 0\). From the equation, \(A=a^2-3, B=-2a, C=-2, H=8, G=2, F=-4\). If…
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