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Pair of Straight Lines — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsPair of Straight Lines2 Marks
MCQ
The value of $\lambda$, for which the equation $x^2-y^2-x-\lambda y-2=0$ represents a pair of straight line, are
  • ✓
    $3,-3$
  • B
    $-3,1$
  • C
    3, 1
  • D
    $-1,1$
✓

Answer

Correct option: A.
$3,-3$
(A) Given equation of pair of lines is $x^2-y^2-x-\lambda y-2=0$
$\therefore \quad a=1, b=-1, c=-2, f=\frac{-\lambda}{2}, g=\frac{-1}{2}, h=0$
Now, $abc +2 fgh - af ^2- bg ^2- ch ^2=0$
$\therefore \quad 2-\frac{\lambda^2}{4}+\frac{1}{4}=0 \Rightarrow \frac{\lambda^2}{4}=\frac{9}{4}$
$\begin{array}{l}\Rightarrow \lambda^2=9 \\ \Rightarrow \lambda= \pm 3\end{array}$

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