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STRAIGHT LINES — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSTRAIGHT LINES1 Mark
MCQ
Choose the correct answer. The tangent of angle between the lines whose intercepts on the axes are a, -b and b, -a, respectively, is
  • A
    $\frac{\text{a}^2-\text{b}^2}{\text{ab}}$
  • B
    $\frac{\text{b}^2-\text{a}^2}{2}$
  • ✓
    $\frac{\text{b}^2-\text{a}^2}{2\text{ab}}$
  • D
    None of these.
✓

Answer

Correct option: C.
$\frac{\text{b}^2-\text{a}^2}{2\text{ab}}$
  1. $\frac{\text{b}^2-\text{a}^2}{2\text{ab}}$
Solution:
Intercepts of line are a and -b; i.e., line passes through the points (a, 0), (0, -b).
$\therefore$ Slope of line, $\text{m}_1=\frac{-\text{b}-0}{0-\text{a}}=\frac{\text{b}}{\text{a}}$
Intercepts of line are b, -a; i.e., line passes through the points (b, 0), (0, -a).
$\therefore$ Slope of line, $\text{m}_2=\frac{-\text{a}-0}{0-\text{b}}=\frac{\text{a}}{\text{b}}$
If $\theta$ is the angle between the lines, then
$\tan=\theta=\frac{\frac{\text{b}}{\text{a}}-\frac{\text{a}}{\text{b}}}{1+\frac{\text{a}}{\text{b}}\times\frac{\text{b}}{\text{a}}}=\frac{\frac{\text{b}^2-\text{a}^2}{\text{ab}}}{2}=\frac{\text{b}^2-\text{a}^2}{2\text{ab}}$

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