https://file.aiquickdraw.com/mathbot/file/1727228483929bktqgxxc.jpg

The problem asks for the equation of an ellipse with the following information:

- The vertex (titik puncak) is at \((13, 0)\).
- One focus \( F_1 \) is at \((13, 0)\) and another \( F_2 \) is at \((12, 0)\).

### Analysis:
1. **Ellipse Equation Form**: For an ellipse with a horizontal major axis, the standard form of the equation is:
   \[
   \frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1
   \]
   where \((h, k)\) is the center, \(a\) is the semi-major axis, and \(b\) is the semi-minor axis. If the foci are horizontally aligned, this suggests that the ellipse's center lies on the same line as the foci.

2. **Focus and Center**: The foci \( F_1(13, 0) \) and \( F_2(12, 0) \) imply that the ellipse has a center between them. Since the foci are very close, the center would be at \( \left( \frac{13 + 12}{2}, 0 \right) = (12.5, 0) \).

3. **Semi-Major Axis \(a\)**: The distance between the center and the vertex gives the semi-major axis length, but it's unclear how to proceed without more geometric clarity from the focus positions.

Would you like a breakdown of how to proceed from here based on these concepts?

Here are 5 questions you might consider next:

1. Would you like to know how to find \(a\) and \(b\) in more detail?
2. Should we explore why the foci are close and how that impacts the equation form?
3. Do you need help interpreting how the vertex affects the major axis in an ellipse?
4. Are there any specific points in the diagram that seem confusing regarding the foci or vertices?
5. Would you like to explore more examples of ellipses with close foci?

**Tip**: Ellipses have two key parameters: the distance between the foci and the length of the major axis. These define their shape!

Elips dengan titik puncak (13, 0) serta fokus F1(13, 0) dan F2(12, 0) memiliki persamaan ....

Find the equation of an ellipse with vertex at (13, 0) and foci F1(13, 0) and F2(12, 0). This problem requires knowledge of conic sections and the standard equation of an ellipse. Suitable for high school students in Grades 10-12.

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