1. A method for automatically aligning a medical instrument relative to a target point in a patient's body using a computed tomography apparatus with fluoroscopy mode, comprising the steps of: (a) positioning a paracentesis tip of the medical instrument at a paracentesis point of the patient's body using an automated guidance system; (b) using said automated guidance system, positioning the medical instrument in a firs position in a CT image plane that contains the paracentesis point; (c) determining and storing spatial coordinates of the medical instrument in said first position; (d) using said automated guidance system, positioning the medical instrument in a second position in said CT image plane that differs from said first position; (e) determining and storing spatial coordinates of the medical instrument in said second position; and (f) determining spatial coordinates of said CT image plane from the spatial coordinates determined and stored in steps (c) and (e).