Q: Car vibrates when braking on a hill.

The front brake rotors on this car is common to get warped causing the vibration you feel. When you are going down the hill it is putting more stress on the brakes and will tend to heat the rotors more. The warped rotors are felt more on a downhill grade and will only get warped worse till you will start to feel it all the time. If you feel it in the steering wheel then it is in the front brake rotors. If you feel it more in the seat of your pants then it is in the rear brakes. It could be felt in both and would be in both the front and rear brakes. I recommend you have a mechanic like one from YourMechanic to inspect your brakes for you.

The vibration that you are feeling is coming from the brake rotors being warped. This can happen over time with the rotors due to normal wear and tear. Applying the brakes going down hill makes the rotors get warmer than they usually do. Heat causes metal to expand and when this happens it makes the warpage bad enough that you can feel the shaking through the car when braking. Once the rotors cool down the warpage is less noticeable. Usually rotors can be machined so the rotors are flat again. It is possible that the rotors may be too worn, or too thin, to machine. I would ask for help from one of the mechanics at YourMechanic so they can come to you and check your rotors. Once they do that they will know whether or not your brakes need to be replaced or machined.