https://r2.erweima.ai/mathbot/image/17262211539308sfv2ybb.jpg

The equation given is the standard form of an ellipse:

\[
\frac{x^2}{9} + \frac{y^2}{49} = 1
\]

From this, we can deduce the key properties of the ellipse:

1. **Semi-major axis**: Since the larger denominator is under \(y^2\), the ellipse is vertically oriented. The semi-major axis is along the y-axis, and its length is \( \sqrt{49} = 7 \).
   
2. **Semi-minor axis**: The semi-minor axis is along the x-axis, with length \( \sqrt{9} = 3 \).

3. **Center**: The center of the ellipse is at the origin \((0,0)\).

### Steps to graph the ellipse:
- The ellipse is centered at the origin.
- The vertices are at the points:
   - On the y-axis: \((0, 7)\) and \((0, -7)\)
   - On the x-axis: \((3, 0)\) and \((-3, 0)\)

From the image, it seems that the current graph is showing a circle (same radii for x and y axes) instead of an ellipse. You need to adjust the red points on the graph to match these coordinates, placing:
- One red point at \((0,7)\),
- One red point at \((0,-7)\),
- One red point at \((3,0)\), and
- One red point at \((-3,0)\).

Do you need further details or have any questions about graphing ellipses?

Here are some related questions you can explore:
1. What is the general form of an ellipse equation?
2. How does the orientation of an ellipse change with respect to its major and minor axes?
3. How do you calculate the eccentricity of an ellipse?
4. What are the foci of an ellipse, and how do you locate them?
5. How can ellipses be applied in real-world contexts like planetary orbits?

**Tip**: When the larger denominator is under \(y^2\), the ellipse is vertical; when it's under \(x^2\), the ellipse is horizontal.

Drag the points to graph the ellipse \( \frac{x^2}{9} + \frac{y^2}{49} = 1 \).

Learn how to graph the ellipse defined by the equation x^2/9 + y^2/49 = 1. Understand the key properties of ellipses, including the semi-major and semi-minor axes, and how to place the points to create an accurate graph. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation