Which condition is characterized by a symmetrically widened periodontal ligament space and a sun-burst appearance on X-ray?

The condition that is characterized by a symmetrically widened periodontal ligament space and a sun-burst appearance on X-ray is osteosarcoma. Osteosarcoma is a malignant bone tumor that typically occurs in the long bones of adolescents and young adults. One of the hallmark radiographic features of osteosarcoma is the sun-burst appearance, which is indicative of the aggressive periosteal reaction due to the tumor's growth pattern. This appearance results from the tumor's ability to produce bone, leading to radiopaque lines that emanate from the surface of the bone like rays of sunshine.

The widening of the periodontal ligament space can be seen in cases where the tumor invades the intricacies of the bone and surrounding tissues, leading to changes in the normal anatomy and a disruption of the periodontal supports. This phenomenon reflects the aggressive nature of osteosarcoma and its tendency to erode the surrounding structures.

In summary, the combination of a symmetrically widened periodontal ligament space and a sun-burst appearance is strongly suggestive of osteosarcoma, making it the correct answer in this context.