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in Limit, continuity and differentiability by (15 points)
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) \( 12 \sqrt{2} \)

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Tangent at(3, -9/2)

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