### 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.

Determine the type of conic section represented by the equation x = 6y + 6, and graph it. What is the type of conic section represented by the equation = 6y + 6? parabola hyperbola ellipse point circle no graph Graph x = 6y + 6. Choose the correct graph below. O A. OB. Oc. OD.

O Graph the ellipse. Give the domain, range, center, vertices, and focus. 49x? + 16y2 + 192y – 208 = 0

Part 1 - Ellipse:  Graph each ellipse and locate the foci.  For full credit, you must show all your work! Graph each ellipse and locate the foci.  For full credit, you must show all your work!