Trong mặt phẳng tọa độ $Oxy$ cho đường thẳng $(d)$ có phương trình $y = kx + k^2 - 3$.
1) Tìm $k$ để đường thẳng $d$ đi qua gốc tọa độ.
2) Tìm $k$ để đường thẳng $(d)$ song song với đường thẳng $(d)$ có phương trình $y = - 2x + 10$
Nhắc lại : Đường thẳng $(d) :  y=ax+b$ song song với đường thẳng $(d') : y=a'x+b'$ khi và chỉ khi $a=a', b\ne b'$.

$1)$ Với $x = 0, y = 0$, ta có $k^2 - 3 = 0$ hay $k^2 = 3$, suy ra $k =\pm\sqrt{3}$.

$2)$  Để đường thẳng $(d)$ song song với đường thẳng $(d')$ thì phải có
$\begin{cases}k = - 2 \\ k^2-3 \ne 10 \end{cases}\Leftrightarrow k = - 2$.

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