This is the 4815th most frequent Japanese word.
注が
"注が" is a conjugated form of the verb "注ぐ," meaning "to pour" or "to flow" in English.
The verb "注がれた" (sosagareta) is a passive form of "注ぐ" (sosogu), meaning "to pour" or "to bestow." Here, it metaphorically indicates how hope was instilled in someone's heart.
私の心に新しい希望が注がれた。
New hope was poured into my heart.
The verb "注いだ" (sosoida) is the past indicative form of "注ぐ" (sosogu). It directly refers to the physical act of pouring a liquid (here, wine) into a container.
彼女はグラスにワインを丁寧に注いだ。
She carefully poured wine into the glass.
"注がれている" (sosagarete iru) is the progressive passive form of "注ぐ" (sosogu), indicating that passion is metaphorically being invested into the plan.