If the normals at an end of a latus rectum of an ellipse passes through the other end of the minor axis, then prove that `e^(4) + e^(2) =1.`

Explanation

To prove that \( e^4 + e^2 = 1 \) under the given conditions, we will follow these steps:

### Step 1: Set up the ellipse
We start with the standard equation of an ellipse with the major axis along the x-axis and the minor axis along the y-axis:
\[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \]
where \( a > b \) and \( e \) is the eccentricity defined as \( e = \sqrt{1 - \frac{b^2}{a^2}} \).
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