Solution to a quadratic Diophantine equation in two variables

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Have been exploring a roundabout solution to a linear Diophantine equation:

$$36x^2y^2+ a^2-2bxy-25(x^2+y^2)=0$$ $$x,y\in\Bbb Z; \qquad0 < x,y$$

where a, b are known positive integers.

Considering the example of:

$$36x^2y^2+ 646^2-7802xy-25(x^2+y^2)=0$$ What is the best approach?