Results on the probability of the existence of rational points on certain families of conics

The three interns present their work done in August under the guidance of Efthymios Sofos.

We prove results on the probability for the conic  aX^^2+bY^^2=cZ^^2 to be solvable, where
a,b,c are odd natural numbers having a prescribed number of prime divisors and do not exceed x.
This work was motivated by a question raised in a recent paper of Nick Rome and Efthymios Sofos.