Eliminate $m$ from the equations $m^{2} x - m y + a = 0, m y + x = 0$ .

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Solution

$m^{2} x - m y + a = 0$ ..... $(i)$
$m y + x = 0$ ..... $(i i)$
$m = \frac{- x}{y}$
Substitute $m$ in $(i)$ , we get
${(\frac{- x}{y})}^{2} x - (\frac{- x}{y}) y + a = 0$
Therefore, the eliminated equation is
$x^{3} + x y^{2} + a y^{2} = 0$

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