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We are asked to find the equation of an ellipse with the following characteristics:
- Center at \( (0, 0) \)
- Foci at \( (-4, 0) \) and \( (4, 0) \)
- Major axis length \( 12 \)

### Step-by-step solution:

1. **Standard Equation of an Ellipse**:
   The general equation of an ellipse with a horizontal major axis is:
   \[
   \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1
   \]
   where:
   - \( a \) is the semi-major axis (half of the total length of the major axis),
   - \( b \) is the semi-minor axis,
   - The distance from the center to each focus is denoted as \( c \), with \( c^2 = a^2 - b^2 \).

2. **Given Information**:
   - The total length of the major axis is 12, so the semi-major axis \( a = 6 \).
   - The distance from the center to each focus is 4, meaning \( c = 4 \).

3. **Find \( b^2 \)**:
   Using the relationship \( c^2 = a^2 - b^2 \):
   \[
   4^2 = 6^2 - b^2
   \]
   \[
   16 = 36 - b^2
   \]
   \[
   b^2 = 36 - 16 = 20
   \]

4. **Final Equation**:
   Now we can write the equation of the ellipse:
   \[
   \frac{x^2}{6^2} + \frac{y^2}{20} = 1
   \]
   \[
   \frac{x^2}{36} + \frac{y^2}{20} = 1
   \]

The correct answer is **D**.

Would you like a detailed explanation on any part of the solution? 

Here are 5 related questions:
1. How do you derive the standard form of an ellipse's equation?
2. What is the difference between the major and minor axes of an ellipse?
3. How can you find the foci of an ellipse from its equation?
4. What are the key characteristics of ellipses compared to circles?
5. How is the eccentricity of an ellipse calculated?

**Tip:** When solving for ellipses, always remember the relationship \( c^2 = a^2 - b^2 \), which connects the semi-major axis, semi-minor axis, and the distance to the foci.

Persamaan elips dengan pusat (0,0), fokus (-4, 0) dan (4, 0) serta Panjang sumbu mayor 12 adalah

Solve the equation of an ellipse with center at (0,0), foci at (-4, 0) and (4, 0), and a major axis length of 12. This problem involves conic sections and geometry, utilizing the standard form of the ellipse equation. Suitable for students in Grades 10-12.

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