Find the equation of hyperbola centered at (0,0), transverse axis horizontal, passing through points (3,5) and (2,-3).

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With this problem, I substuted the given points to the standard form of a horizontal hyperbola, $$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$$

and got $$\frac{3^2}{a^2}-\frac{5^2}{b^2}=1→\frac{9}{a^2}-\frac{25}{b^2}=1 $$ $$\frac{2^2}{a^2}-\frac{-3^2}{b^2}=1→ \frac{4}{a^2}-\frac{9}{b^2}=1$$

What should I do next?

Thank you very much!

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Hint: You have $2$ equations in the $2$ unknowns of $a^2$ and $b^2$. The usual thing to try to do is to eliminate one of the variables so you can then solve for the other variable. You can do that here by, for example, subtracting $4$ times the first equation from $9$ times the second equation to eliminate the term with $a^2$.