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The given problem asks to find the standard equation of an ellipse, where:

- The ends of the major axis are \( (0, \pm 9) \).
- The ends of the minor axis are \( (\pm 3, 0) \).

From this information, we can conclude the following:

1. **Center of the Ellipse**: Since the axes are centered on the origin and the given points are symmetric about the origin, the center of the ellipse is \( (0, 0) \).

2. **Length of the Major Axis**: The major axis runs vertically (because the \( y \)-coordinates vary more). The distance from the center to the endpoints of the major axis is 9. Therefore, the length of the semi-major axis \( a = 9 \).

3. **Length of the Minor Axis**: The minor axis runs horizontally (since the \( x \)-coordinates vary in the minor axis points). The distance from the center to the endpoints of the minor axis is 3. Therefore, the length of the semi-minor axis \( b = 3 \).

### Standard Equation of an Ellipse:
The standard form of the equation for an ellipse with a vertical major axis is:

\[
\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1
\]

Substituting \( a = 9 \) and \( b = 3 \):

\[
\frac{x^2}{3^2} + \frac{y^2}{9^2} = 1
\

Write the standard equation of ellipse with the given features. Ends of major axis (0,±9), and ends of minor axis (±3,0)

Learn how to derive the standard equation of an ellipse given the ends of its major axis at (0, ±9) and minor axis at (±3, 0). This problem covers key concepts in analytic geometry and conic sections, including the formula for the equation of an ellipse. Suitable for Grades 10-12.

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