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A line has intercepts a, b on the axes when the axes are rotated through an angle $α$ , the line makes equal intercepts on axes then $\tan α =$

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$(\frac{a + b}{a - b})$

$(\frac{a - b}{a + b})$

$(\frac{a}{b})$

$(\frac{b}{a})$

answer is B.

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Detailed Solution

$\frac{x}{a} + \frac{y}{b} = 1$

$\frac{(X \cos α - Y \sin α)}{a} + \frac{(X \sin α + Y \cos α)}{b} = 1$
x. coefficient = y coefficient
$\begin{array}{l} (a - b) \cos α = (a + b) \sin α \\ \Rightarrow \tan α = \frac{a - b}{a + b} \end{array}$

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