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9. straight line — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS9. straight line1 Mark
MCQ
Angle between the lines $\frac{x}{a} + \frac{y}{b} = 1$ and $\frac{x}{a} - \frac{y}{b} = 1$ is
  • ✓
    $2{\tan ^{ - 1}}\frac{b}{a}$
  • B
    ${\tan ^{ - 1}}\frac{{2ab}}{{{a^2} + {b^2}}}$
  • C
    ${\tan ^{ - 1}}\frac{{{a^2} - {b^2}}}{{{a^2} + {b^2}}}$
  • D
    None of these
✓

Answer

Correct option: A.
$2{\tan ^{ - 1}}\frac{b}{a}$
a
(a)The lines are $bx + ay - ab = 0$ and $bx - ay - ab = 0$.

Hence the required angle is

${\tan ^{ - 1}}\left| {\frac{{ab - ( - ab)}}{{{b^2} + ( - {a^2})}}} \right| = {\tan ^{ - 1}}\left| {\frac{{2ab}}{{{b^2} - {a^2}}}} \right| = 2{\tan ^{ - 1}}\frac{b}{a}$.

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