Question

Determinati m care apartine lui R pentru care dreptele d1:2x+y=0 si d2:x+my+2017=0 sunt paralele

Answer 1

[tex]\text{Doua drepte sunt paralele daca au pantele egale:}\\ d_1:2x+y=0 \\ y=-2x\Rightarrow m_{d_1}=-2\\ \\ d_2:x+my+2017=0\\ my=-x-2017\\ y=\dfrac{-1}{m}\cdot x-\dfrac{2017}{m}\Rightarrow m_{d_2}=\dfrac{-1}{m}\\ \text{Din conditia ca pantele sa fie egale se obtine:}\\ \dfrac{-1}{m}=-2\Rightarrow \boxed{m=\dfrac{1}{2}} [/tex]