If \( 3\sqrt{2}x - 4y = 12 \) is a tangent to the hyperbola \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\) and \(\frac{5}{4}\) is its eccentricity, then \( a^2 - b^2 = \)
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For a hyperbola \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\), tangent: \( y = mx \pm \sqrt{a^2 m^2 - b^2} \). Eccentricity: \( e^2 = 1 + \frac{b^2}{a^2} \).