Can you move an object in unity by maintaining a standard distance from the camera?

I'm a newbie unity user and I'm working on a Basket shoot simulator in Hololens2. Right now I'm working on a button that, when pressed should move the hoop where the camera is looking but it needs to have the Pos Y = 3 and be 4,5 meters away from the camera (since those are the measures in meters for a free throw in basketball).

I've tried to use camera.transform.forward but in no way I was able to set the free throw distances that i need from the camera, especially the Y. The method was this:

public GameObject hoop;
public new GameObject camera;

float freeThrowY = 3;
float freeThrowZ = (float) 4.5;

public void ChangeHoop ()
{
    hoop.transform.position = transform.position + camera.transform.forward * freeThrowY * freeThrowZ;
}

and the hoop was very far obviously, so I tried doing this:

hoop.transform.position = camera.transform.forward + new Vector3(camera.transform.position.x, freeThrowY, freeThrowZ); 

But the hoop just stays in basically the same position, changing from around 0 to 1 meters. (The hoop does move, so the button works)

I also tried:

hoop.transform.position = new Vector3(camera.transform.forward.x, camera.transform.forward.y + freeThrowY, camera.transform.forward.z + freeThrowZ);

But same problem as before.

I've searched for 2 days online but none of the solutions worked for me, so I guess I'm missing something probably very simple.

Thank you for helping (sorry for the english, if something is not clear I'll try to explain it better)

First you need to get the cameras forward vector without any x/z rotation.
Once that forward vector is aligned with the ground plane, you can multiply it by "distanceAway".

var forward = Vector3.Cross(camera.transform.right, Vector3.up);
var position = transform.position + forward * distanceAway;

Then set the positions y component to your "distanceUp" value, and assign the final position to your hoop.

position.y = distanceUp;

hoop.transform.position = position;