MCQ
The points on the X-axis whose perpendicular distance from the line $\frac{x}{a}+\frac{y}{b}=1$ is a, are
  • $\left[\frac{ a }{ b }\left( b \pm \sqrt{ a ^2+ b ^2}\right), 0\right]$
  • B
    $\left[\frac{ b }{ a }\left( b \pm \sqrt{ a ^2+ b ^2}\right), 0\right]$
  • C
    $\left[\frac{ a }{ b }\left( a \pm \sqrt{ a ^2+ b ^2}\right), 0\right]$
  • D
    None of these

Answer

Correct option: A.
$\left[\frac{ a }{ b }\left( b \pm \sqrt{ a ^2+ b ^2}\right), 0\right]$
(A)
Let the point be $(h, 0)$, then $a=\left|\frac{b h+0-a b}{\sqrt{a^2+b^2}}\right|$
$\Rightarrow bh = \pm a \sqrt{ a ^2+ b ^2}+ ab$
$\Rightarrow h =\frac{ a }{ b }\left( b \pm \sqrt{ a ^2+ b ^2}\right)$
Hence, the points are $\left\{\frac{a}{b}\left(b \pm \sqrt{a^2+b^2}\right), 0\right\}$.

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