Give me two equations of ellipse with the center (0,0) for me to solve

Here are two equations of ellipses centered at \((0, 0)\) for you to solve:

1. \(\frac{x^2}{16} + \frac{y^2}{9} = 1\)

2. \(\frac{x^2}{25} + \frac{y^2}{4} = 1\)

Would you like to solve these equations or need any details about them?

Here are 5 related questions for further exploration:

1. How do you determine the lengths of the major and minor axes from the equation of an ellipse?
2. What is the eccentricity of each ellipse, and how is it calculated?
3. Can you graph each ellipse based on the given equations?
4. How do the foci of each ellipse relate to the lengths of the axes?
5. What happens to the ellipse if the denominators in the equations are changed?

**Tip:** For ellipses, the sum of the distances from any point on the ellipse to the two foci is always constant.

Explore how to solve equations of ellipses centered at (0, 0) with detailed explanations and examples. Learn about the properties of ellipses, including their equations, major and minor axes lengths, and eccentricity. Suitable for students in Grades 10-12.

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