Question

Giúp e vs ạ

Answer 1

Chọn \(A\left(0;2\right)\) và \(B\left(1;5\right)\) là 2 điểm thuộc Q

Gọi \(\overrightarrow{v}=\left(a;b\right)\)

\(\left\{{}\begin{matrix}T_{\overrightarrow{v}}\left(A\right)=C\\T_{\overrightarrow{v}}\left(B\right)=D\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}C\left(a;b+2\right)\\D\left(a+1;b+5\right)\end{matrix}\right.\)

\(C;D\in\left(P\right)\Rightarrow\left\{{}\begin{matrix}b+2=a^2\\b+5=\left(a+1\right)^2\end{matrix}\right.\)

\(\Rightarrow3=\left(a+1\right)^2-a^2\)

\(\Rightarrow2a=2\Rightarrow a=1\)

\(\Rightarrow b=-1\)

Vậy \(T_{\overrightarrow{v}}\left(Q\right)=\left(P\right)\) với \(\overrightarrow{v}=\left(1;-1\right)\)