https://file.aiquickdraw.com/mathbot/file/1727052695900qmzzd277.jpg

Let's analyze the given equation:

\[
\frac{2x^2}{25} + \frac{(y - 3)^2}{49} = 1
\]

We can rewrite this as:

\[
\frac{x^2}{\frac{25}{2}} + \frac{(y - 3)^2}{49} = 1
\]

This equation is in the form:

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

When \(a^2\) and \(b^2\) are positive, this represents an ellipse if \(a^2 \neq b^2\) or a circle if \(a^2 = b^2\).

Here:
- \(a^2 = \frac{25}{2}\)
- \(b^2 = 49\)

Since \(\frac{25}{2} \neq 49\), this is **not** a circle. Therefore, the correct answer is **Ellipse**.

Would you like further details or have any other questions?

### Related Questions:
1. How do you convert an ellipse equation from general form to standard form?
2. How do you distinguish between an ellipse and a hyperbola?
3. What are the properties of an ellipse, such as foci and eccentricity?
4. How can you identify a parabola from a given equation?
5. How do you find the center and axes lengths of an ellipse?

**Tip:** The standard form of an ellipse equation always has the format \(\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1\), where \((h, k)\) is the center.

Which shape is defined by the equation (2x^2)/25 + (y-3)^2/49 = 1?

Learn how to identify the shape defined by the equation (2x^2)/25 + (y-3)^2/49 = 1. This problem involves key concepts from analytic geometry and conic sections, particularly ellipses. Understand the form of the equation, the role of the major and minor axes, and how to recognize an ellipse.

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