MCQ
The angle between the lines whose intercepts on the axes are (a, -b) and (b, -a) respectively, is
  • A
    $\tan ^{-1} \frac{a^2+b^2}{a b}$
  • B
    $\tan ^{-1} \frac{b^2-a^2}{2}$
  • $\tan ^{-1} \frac{b^2-a^2}{2 a b}$
  • D
    $\tan ^{-1} \frac{b^2-a^2}{a b}$

Answer

Correct option: C.
$\tan ^{-1} \frac{b^2-a^2}{2 a b}$
(C)Equation of lines are $\frac{x}{ a }-\frac{y}{b}=1$ and $\frac{x}{b}-\frac{y}{ a }=1$
$\Rightarrow m _1=\frac{ b }{ a }$ and $m _2=\frac{ a }{ b }$
$\therefore \quad \theta=\tan ^{-1}\left|\frac{\frac{b}{a}-\frac{a}{b}}{1+\frac{b}{a} \cdot \frac{a}{b}}\right|=\tan ^{-1} \frac{b^2-a^2}{2 a b}$

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