Police, who arrested one man at the scene, are appealing for witnesses after one person suffered a serious leg injury and another is at Leeds General Infirmary being treated for a serious head injury.
The collision happened shortly before 4.45pm yesterday at the junction of Canterbury Avenue and Dawnay Road, and involved a grey Skoda Rapid and a blue and white Yamaha Raptor quad bike.
A West Yorkshire Police spokesperson said: "Both the driver and passenger on the quad bike were thrown from the vehicle as a result of the collision.
"One suffered a serious leg injury and the other is at Leeds General Infirmary being treated for a serious head injury.
"A 54-year-old man was arrested at the scene on suspicion of causing serious injury by dangerous driving and has been released under investigation."
"Police are keen to speak to anyone who witnessed the collision itself or the manner of driving of either vehicle immediately prior to the collision. Any information can be passed to PC 2561 Spencer in the Roads Policing Unit via 101, quoting log 1289 of 20/04."