fix $a$ and $b$ as rational numbers. If $x,y$ and $t$ be variable then how can I have a parametrization solution to this equation?
$$4ax^2+4by^2=3t^2$$
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The formula in General there. http://math.stackexchange.com/questions/738446/solutions-to-ax2-by2-cz2/738527#738527 – individ Mar 03 '15 at 05:16
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there need not be any rational solutions whatsoever (other than $x=y=t=0$), for example $a=b=1$ – Will Jagy Mar 03 '15 at 05:38
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If talking about the equation. $$ax^2+by^2=3cz^2$$ decisions on these formulas can easily record selecting $c$ so that any of the $3c(a+b)$ ; $a(3c-b)$ ; $b(3c-a)$ was square. – individ Mar 03 '15 at 06:25