Redundancy in solutions to a Diophantine equation.

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enter image description here Here, they write the solution with both (4d,d) and (12d,3d) and similarly (d,d) and (5d,5d).

Aren't these two sets redundant as the second can be expressed as the first as d varies over the integers?

The solution I obtained was (a,a) ,(4a,a) and (19a,a); $$a\in\mathbb{Z}$$. Is this correct?