I would appreciate it if someone could recommend a solution for my problem.
I have approached our local security company but after a year of them not responding I'm going "public".

We have one of those automatic gates on our driveway. There is a keypad by the gate which can be used to open/close the gate with a PIN and there is a button which when pressed sounds a buzzer in the house. There is no intercom or video. There is also a light-beam across the drive which when broken also activates the buzzer in the house (handy for letting you know someone or something has crossed through the gateway), this only works when the gate is open. The gate can be operated via the keypad by the gate, via remotes which we typically keep in the car, or by a button inside the house. The house is set back from the gate, distance 30-40m.

The problem now being that foliage has grown and we can no longer see the gate from the  front door of the house. Or indeed from anywhere inside the house. To the point where we now have to walk almost to the gate to see whether it is open or closed. Sure the easy answer is chop down the foliage, but we kind of like the privacy it affords from the road, but wouldn't be helpful at night time anyway. We are residential, and the gateway area is covered by street lighting so its never completely dark.

This leads to the all too common scenario in our house that when the buzzer goes off, we aren't sure if someone has crossed the gateway or has pushed the button because we often are not sure if the gate is closed or not. Its like Schrodingers gate. 

So we need a simple way of knowing from inside the house whether the gate is actually open or not.

I'm presuming a camera that links to a screen in the house may be suitable, but I'm concerned about the distance the camera would have to cover. The best view of the gate from the house would be from a vantage point that is 40m away. There is another position about 30m away which would require a lot more pruning.

First and foremost any solution would need to be able to provide an easy view from inside the house of the gate simply to see if its closed or open. 
But while we are looking at such systems, perhaps we could factor in some security features like motion sensing and recording.

I look forward to your suggestions.