### Graphing the Ellipse Given the equation of the ellipse: \[ 25x^2 + 9y^2 = 225 \] **Steps to Graph the Ellipse:** 1. **Standard Form of Ellipse Equation:** - First, rewrite the equation in standard form by dividing all terms by 225: \[ \frac{x^2}{9} + \frac{y^2}{25} = 1 \] 2. **Identify the Axes and Center:** - The equation is now in the form \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\), where \( a^2 = 9 \) and \( b^2 = 25 \). - The center of the ellipse is at the origin (0,0). - \( a = 3 \) (horizontal semi-axis) and \( b = 5 \) (vertical semi-axis). 3. **Determine the Orientation:** - Since \( b > a \), the major axis is vertical. 4. **Plot the Major and Minor Axes:** - Vertical Axis: Extend 5 units up and down from the center, reaching the points (0,5) and (0,-5). - Horizontal Axis: Extend 3 units left and right from the center, reaching the points (3,0) and (-3,0). 5. **Draw the Ellipse:** - Connect these extremities in a smooth, oval shape to form an ellipse. **Graph Description:** - The graph includes a Cartesian coordinate system with labeled axes. - The x-axis ranges from -8 to 8, and the y-axis ranges from -8 to 8, with a grid to aid in plotting points precisely. - The ellipse is centered at the origin and stretches further along the y-axis than the x-axis, reflecting the semi-axis lengths identified earlier.

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