If 2y – $a^{2}$ x = 3 and 2y – (4ax +1) = 0 are parallel, find the value of a, where a is a natural number.

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Solution

y = ( $a^{2}$ /2)x +3/2 and y = (4a/2)x +1/2
$\Rightarrow$ $m_{1}$ = $a^{2}$ /2, $m_{2}$ = 2a
Since, lines are parallel
$m_{1}$ = $m_{2}$
$\Rightarrow$ $a^{2}$ /2 = 2a
$\Rightarrow$ a = 4

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