3. If the line \( x-2 y=12 \) is tangent to the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) at the point \( \left(3, \frac{-9}{2}\right) \), then the length of the latusrectum of the ellipse is
(a) \( 8 \sqrt{3} \)
(b) 9
(2019 Main, 10 Aprill)
(d) \( 12 \sqrt{2} \)