Find the eccentricity, foci and the length of the latusrectum of the ellipse `x^2+4y^2+8y-2x+1=0.`

Explanation

To solve the given problem, we will follow these steps:

### Step 1: Rewrite the given equation
We start with the equation of the ellipse:
\[ x^2 + 4y^2 + 8y - 2x + 1 = 0 \]

### Step 2: Rearranging the equation
We can rearrange the equation by grouping the \(x\) and \(y\) terms:
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