Có: \(\left\{{}\begin{matrix}\frac{a}{k}=\frac{x}{a}\\\frac{b}{k}=\frac{y}{b}\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}a^2=kx\\b^2=ky\end{matrix}\right.\\ \Rightarrow\frac{a^2}{b^2}=\frac{kx}{ky}=\frac{x}{y}\)
Ta có:
\(\left\{{}\begin{matrix}\frac{a}{k}=\frac{x}{a}\Rightarrow a^2=kx\\\frac{b}{k}=\frac{y}{b}\Rightarrow b^2=ky\end{matrix}\right.\)
Chia theo vế ta được:
\(a^2:b^2=kx:ky\)
\(\Rightarrow\frac{a^2}{b^2}=\frac{kx}{ky}\)
\(\Rightarrow\frac{a^2}{b^2}=\frac{x}{y}\left(đpcm\right).\)
Chúc bạn học tốt!