Mathematics

Problem

If the line

x - 2y = 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 latus rectum of the ellipse is (a)

8\sqrt{3}

12\sqrt{2}