If the lines $2 y - a^{2} x = 3$ and $2 y - (4 a x + 1) = 0$ are parallel, find the value of a.

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Solution

The slope of the given lines $2 y - a^{2} x = 3$ and $2 y - (4 a x + 1) = 0$ are -
$y = \frac{a^{2} x}{2} + \frac{3}{2} a n d y = \frac{4 a x}{2} + \frac{1}{2}$ $[1 m a r k]$
Here, $m_{1} = \frac{a^{2}}{2}$
and $m_{2} = 2 a$ $[1 m a r k]$
Since lines are parallel
$m_{1} = m_{2}$
$\Rightarrow \frac{a^{2}}{2} = 2 a \Rightarrow a = 4$ $[1 m a r k]$

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