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Question
The tangent of angle between the lines whose intercepts on the axes are a, – b and b, – a, respectively, is ______.
Options
`(a^2 - b^2)/(ab)`
`(b^2 - a^2)/2`
`(b^2 - a^2)/(2ab)`
None of these
Solution
The tangent of angle between the lines whose intercepts on the axes are a, – b and b, – a, respectively, is `(b^2 - a^2)/(2ab)`.
Explanation:
First equation of line having intercepts on the axes
a, – b is `x/a - y/b` = 1
⇒ bx – ay = ab ......(i)
Second equation of line having intercepts on the axes
b, – a is `x/b - y/a` = 1
⇒ ax – by = ab .....(ii)
Slope of equation (i) m1 = `b/a`
Slope of equation (ii) m2 = `a/b`
∴ tan θ = `|(m_1 - m_2)/(1 + m_1m_2)|`
= `(b/a - a/b)/(1 + a/b b/a)`
= `(b^2 - a^2)/(2ab)`
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