Help with Instantiate and parents

When I Instantiate an object, it does not spawn where the parent is, but where the parent first spawned. I have tried to find out a way to set the Instantiated object’s parent, but I can’t seem to figure it out. Thanks for any help.

void OnTriggerEnter2D (Collider2D shoot) {
		Vector2 myTransform  = player.transform.position - transform.position;
		Rigidbody2D clone;

		Vector3 offset = transform.position;
		offset.x = -0.1f;


		if (shoot.gameObject.tag == "Player") {
			clone = Instantiate (bullet, offset, transform.rotation) as Rigidbody2D;
			clone.velocity = transform.TransformDirection (myTransform * 2.5f);

What happens if you change it to the following?

Vector3 offset = new Vector3(-0.1f,0,0);
 clone = Instantiate (bullet, transform.position + offset, transform.rotation) as Rigidbody2D;