Q194 / 270 · NDA 2012 (Phase 2) · Mathematics

What is the perpendicular distance between the parallel $3 x+4 y=9$ and $9 x+12 y+28=0$ ?

A
$7 / 3$ units
B
$8 / 3$ units
C
$10 / 3$ units
Correct answer
D
$11 / 3$ units

Solution

$3 x+4 y-9=0$\ldots(1) $3 x+4 y+\frac{28}{3}=0$\ldots(2) distance between parallel lines $=\frac{\left|\frac{28}{3}+9\right|}{\sqrt{3^2+4^2}}$ $\Rightarrow \frac{55}{15} \Rightarrow \frac{11}{3}$ units.

Hence, the correct answer is option: 'D'.

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