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 find the eccentricity, center, vertices, foci, minor axis, major axis, directrices, and latus rectum of the ellipse given by the equation \( 25x^2 + 9y^2 - 150x - 90y + 225 = 0 \), we will follow these steps:

### Step 1: Rearrange the equation
We start with the equation:
\[ 25x^2 + 9y^2 - 150x - 90y + 225 = 0 \]
Rearranging gives:
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