The angle between the lines whose intercepts on the axes are a, -… - Vidyadip

MCQ

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

A
${\tan ^{ - 1}}\frac{{{a^2} - {b^2}}}{{ab}}$
B
${\tan ^{ - 1}}\frac{{{b^2} - {a^2}}}{2}$
✓
${\tan ^{ - 1}}\frac{{{b^2} - {a^2}}}{{2ab}}$
D
None of these

✓

Answer

Correct option: C.

${\tan ^{ - 1}}\frac{{{b^2} - {a^2}}}{{2ab}}$

c
(c)Equation of lines are $\frac{x}{a} - \frac{y}{b} = 1$and $\frac{x}{b} - \frac{y}{a} = 1$

==> ${m_1} = \frac{b}{a}$and ${m_2} = \frac{a}{b}$

Therefore $\theta = {\tan ^{ - 1}}\frac{{\frac{b}{a} - \frac{a}{b}}}{{1 + \frac{b}{a}.\frac{a}{b}}} = {\tan ^{ - 1}}\frac{{{b^2} - {a^2}}}{{2ab}}$.

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