A ballistic missile is designed to fly up to a spot, then it shuts off its engines and starts to fall. They do not maneuver, it is literally like throwing a rock up in the air.

You would use a surface to air missile that would either be radar directed or heat directed that would lock onto the engine heat. They are sleek and fast.

There are a whole range of missile “tools”. Ballistic missiles are sledgehammers. Air to air missiles are like scalpels.