In these lines, Aegeus appears to understand the importance of the oath Medea is asking for. He says he thinks it's a smart decision, suggesting he admires her ability to plan strategically. He's showing that he's prepared to support her when she needs it by offering to help. Aegeus also suggests a practical approach to the matter by hinting at the benefit this oath would bring him against his own enemies. His search for answers on who it is to swear by shows his awareness of the importance of oaths within their society. It's like he's confirming his dedication to the vow he's about to make by making sure the pledge he swears will be enforced and honored by the almighty.