Question

urgent!!!!!!!!!!!!!!!!​

Answer 1

Răspuns:

Explicație pas cu pas:

Answer 2

$\it a)\ AB=5 \Rightarrow AB^2=5^2 \Rightarrow (x_B-x_A)^2+(y_B-y_A)^2=25 \Rightarrow \\ \\ \Rightarrow (4-a+1)^2+(4+a-2)^2=25 \Rightarrow (5-a)^2+(2+a)^2=25 \Rightarrow \\ \\ \Rightarrow 25-10a+a^2+4+4a+a^2-25=0 \Rightarrow 2a^2-6a+4=0|_{:2} \Rightarrow \\ \\ a^2-3a+2=0 \Rightarrow a^2-a-2a+2=0 \Rightarrow a(a-1)-2(a-1)=0 \Rightarrow \\ \\ \Rightarrow (a-1)(a-2)=0 \Rightarrow \begin{cases}\it a-1=0 \Rightarrow a_1=1\\ \\\it a-2=0 \Rightarrow a_2=2\end{cases}$

$\it b)\ d:\ 2x+3y-12=0\\ \\ B(4-a,\ 4+a)\in d \Rightarrow 2(4-a)+3(4+a)-12=0 \Rightarrow \\ \\ \Rightarrow 8-2a+12+3a-12=0 \Rightarrow a+8=0 \Rightarrow a=-8$

$\it c)\ d:\ 2x+3y-12=0 \Rightarrow y=-\dfrac{2}{3}x+4 \Rightarrow m_d=-\dfrac{2}{3}\\ \\ d':\ y=mx+n,\ \ d'||d \Rightarrow m=m_d=-\dfrac{2}{3} \Rightarrow d':\ y=-\dfrac{2}{3}x+n\ \ \ \ \ (*)\\ \\ A(-1,\ 2)\in d'\ \stackrel{(*)}{\Longrightarrow} 2=-\dfrac{2}{3}\cdot(-1)+n \Rightarrow 2=\dfrac{2}{3}+n \Rightarrow n=2-\dfrac{2}{3}=\dfrac{4}{3}\Rightarrow \\ \\ \Rightarrow d':\ y=-\dfrac{2}{3}x+\dfrac{4}{3} \Rightarrow d':\ 2x+3y-4=0$