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The equation given is:

\[
\frac{(x - 3)^2}{10} + \frac{(y + 4)^2}{9} = 1
\]

This is the standard form of the equation of an ellipse, which is:

\[
\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1
\]

In this form, \((h, k)\) represents the center of the ellipse. Comparing the given equation to the standard form, we can see that:

- \(h = 3\)
- \(k = -4\)

Thus, the center of the ellipse is at \((3, -4)\).

### Correct answer: \((3, -4)\)

Do you have any other questions or would you like more details?

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Here are 5 related questions:
1. How do you find the lengths of the major and minor axes of the ellipse?
2. What do the values of \(a^2\) and \(b^2\) represent in the standard ellipse equation?
3. How do you determine whether the ellipse is horizontal or vertical?
4. Can you explain how to find the foci of an ellipse?
5. What happens to the shape of the ellipse if \(a = b\)?

**Tip:** In ellipse equations, the center can be quickly identified by looking at the shifts \(h\) and \(k\) in the squared terms.

What is the coordinate of the center if ellipse (x - 3)^2 / 10 + (y + 4)^2 / 9 = 1?

Learn how to determine the center of an ellipse from the equation (x - 3)^2 / 10 + (y + 4)^2 / 9 = 1. This problem covers essential concepts in analytic geometry and is suitable for students in Grades 10-12.

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