The points on the x-axis whose perpendicular distance from the li… - Vidyadip

MCQ

The points on the $x$-axis whose perpendicular distance from the line $\frac{x}{a} + \frac{y}{b} = 1$ is a, are

✓
$\left[ {\frac{a}{b}(b \pm \sqrt {{a^2} + {b^2}} ),\,0} \right]$
B
$\left[ {\frac{b}{a}(b \pm \sqrt {{a^2} + {b^2}} ),\,0} \right]$
C
$\left[ {\frac{a}{b}(a \pm \sqrt {{a^2} + {b^2}} ),\,0} \right]$
D
None of these

✓

Answer

Correct option: A.

$\left[ {\frac{a}{b}(b \pm \sqrt {{a^2} + {b^2}} ),\,0} \right]$

a
(a) Let the point be $(h,0)$, then $a = \pm \frac{{bh + 0 - ab}}{{\sqrt {{a^2} + {b^2}} }}$

==> $bh = \pm a\sqrt {{a^2} + {b^2}} + ab \Rightarrow h = \frac{a}{b}(b \pm \sqrt {{a^2} + {b^2}} )$

Hence the point is $\left\{ {\frac{a}{b}(b \pm \sqrt {{a^2} + {b^2}} ),0} \right\}$.

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