The area of the quadrilateral formed by the tangents at the endpoints of the latus rectum of the ellipse $\frac{x^2}{9} + \frac{y^2}{5} = 1$ is:
Step-by-Step Solution
Key Concept: $a = 3$, $b^2 = 5$, $c = 2$. Latus rectum endpoints at $(\pm 2, \pm 5/3)$. Tangent at $(2, 5/3)$: $2x/9 + (5/3)y/5 = 1 \Rightarrow 2x + 3y = 9$. The four tangents form a rhombus with diagonals 6 (vertical) and 9 (horizontal): area $= \frac{1}{2} \times 6 \times 9 = 27$.
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Correct Answer: (3)