Find the separate equations of the lines represented by the equation.
$3 x^{2} - 10 x y - 8 y^{2} = 0$

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Solution

The given equation in
$3 x^{2} - 10 x y - 8 y^{2} = 0$
$\Rightarrow 3 x^{2} - 12 x y + 2 x y - 8 y^{2} = 0$
$\Rightarrow 3 x (x - 4 y) + 2 y (x - 4 y) = 0$
$\Rightarrow (x - 4 y) (3 x - 2 y) = 0$
$\Rightarrow x - 4 y = 0$
and $3 x + 2 y = 0$
Hence, the separate equations of the lines represented by the equation
$3 x^{2} - 10 x y - 8 y^{2} = 0$ are $x - 4 y = 0$ and $3 x + 2 y = 0$ .

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