The area (in sq. units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipse `` `(x^2)/9+(y^2)/5=1` , is: (1) `(27)/4` (2) 18 (3) `(27)/2` (4) 27

Options

A. `27//4`
B. 18
C. `27//2`
D. 27

Explanation

To find the area of the quadrilateral formed by the tangents at the endpoints of the latus rectum to the ellipse given by the equation \(\frac{x^2}{9} + \frac{y^2}{5} = 1\), we can follow these steps:

### Step 1: Identify the parameters of the ellipse
The given ellipse can be compared with the standard form \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\). Here, we have:
- \(a^2 = 9\) → \(a = 3\)
- \(b^2 = 5\) → \(b = \sqrt{5}\)

### Step 2: Calculate the eccentricity \(e\)
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