Find the eccentricity, centre, vertices, foci, minor axis, major axis, directrices and latus-rectum of the ellipse `25 x^2+9y^2-150 x-90 y+225=0.`

Explanation

To solve the problem step by step, we will start by rewriting the given equation of the ellipse and then proceed to find the required properties.

### Step 1: Rewrite the equation of the ellipse
The given equation is:
\[ 25x^2 + 9y^2 - 150x - 90y + 225 = 0 \]

### Step 2: Rearranging the equation
Rearranging gives:
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