`(x^(2))/(36)+(y^(2))/(16)=1`

Explanation

To solve the given equation of the ellipse \(\frac{x^2}{36} + \frac{y^2}{16} = 1\), we will find the coordinates of the foci, the vertices, the lengths of the major and minor axes, the eccentricity, and the length of the latus rectum step by step.

### Step 1: Identify the values of \(a^2\) and \(b^2\)
The standard form of the ellipse is given by:
\[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \]
From the equation \(\frac{x^2}{36} + \frac{y^2}{16} = 1\), we can identify:
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