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Pair of Straight Lines — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsPair of Straight Lines2 Marks
MCQ
The angle between the lines represented by the equation $x^2-2 p x y$$+y^2=0$, is
  • ✓
    $\sec ^{-1} p$
  • B
    $\cos ^{-1} p$
  • C
    $\tan ^{-1} p$
  • D
    $\sin ^{-1} p$
✓

Answer

Correct option: A.
$\sec ^{-1} p$
(A) Given equation of pair of lines is $x^2-2 p x y+y^2=0$
$\therefore \quad a=1, h=-p, b=1$
$\therefore \quad \tan \theta=\left|\frac{2 \sqrt{h^2-a b}}{a+b}\right|$
$\Rightarrow \tan \theta=\frac{ \pm 2 \sqrt{ p ^2-1}}{1+1}= \pm \sqrt{ p ^2-1}$
$\begin{array}{l}\Rightarrow \tan ^2 \theta= p ^2-1 \\ \Rightarrow \sec ^2 \theta-1= p ^2-1 \\ \Rightarrow \theta=\sec ^{-1} p \end{array}$

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