The angle between the lines whose intercepts on the axes are a, -b and b, a respectively, is

t a n^{-} 1 (\frac{b^{2} - a^{2}}{2})

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t a n^{-} 1 (\frac{a^{2} - b^{2}}{a b})

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t a n^{-} 1 (\frac{b^{2} - a^{2}}{2 a b})

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none of these

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Solution

The correct option is D none of these
$L_{1} : x / a + y / - b = 1$ slope $= (- 1 / a) / (\frac{1}{- b}) = b / a$
$L_{2} : x / b + y / a = 1$ slope $= - (1 / b) / (1 / b) = - a / b$
Angle between $L_{1}$ & $L_{2}, t a n θ = \frac{\frac{b}{a} - (\frac{- a}{b})}{1 + \frac{b}{a} (\frac{- a}{b})} = \frac{b^{2} + a^{2}}{a b (0)} = \infty$
$\Rightarrow θ = π / 2$
$\Rightarrow (D)$

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Similar questions

\frac{a^{2} - b^{2}}{a b}

\frac{b^{2} - a^{2}}{2}

\frac{b^{2} - a^{2}}{2 a b}

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(a_{1} + i b_{1}) (a_{2} + i b_{2}) . . . (a_{n} + i b_{n}) = A + i B

{tan}^{- 1} \frac{b_{1}}{a_{1}} + {tan}^{- 1} \frac{b_{2}}{a_{2}} + . . . {tan}^{- 1} \frac{b_{n}}{a_{n}} =

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