Question 1199602
**1. Determine the value of 'a'**

* The vertices are at (±2, 0), which indicates that the major axis lies along the x-axis.
* The distance from the center (0, 0) to a vertex is the length of the semi-major axis (a).
* Therefore, a = 2

**2. Determine the value of 'c'**

* Eccentricity (e) = c/a 
* where:
    * e = eccentricity (2/7)
    * c = distance from the center to a focus 
    * a = semi-major axis (2)

* 2/7 = c / 2
* c = 4/7

**3. Determine the value of 'b'**

* The relationship between a, b, and c in an ellipse is:
    * c² = a² - b²

* (4/7)² = 2² - b²
* 16/49 = 4 - b²
* b² = 4 - 16/49 
* b² = 176/49
* b = √(176/49) = (4√11) / 7 

**4. Write the equation of the ellipse**

* The standard equation of an ellipse centered at the origin with the major axis along the x-axis is:
    * x²/a² + y²/b² = 1

* Substitute the values of a² and b²:
    * x²/2² + y²/[(4√11)/7]² = 1
    * x²/4 + y²/(176/49) = 1
    * x²/4 + 49y²/176 = 1

**Therefore, the equation of the ellipse is x²/4 + 49y²/176 = 1**

**Sketching the Ellipse**

1. **Plot the center:** (0, 0)
2. **Plot the vertices:** (2, 0) and (-2, 0)
3. **Determine the endpoints of the minor axis:** 
    * Since b = (4√11)/7, the endpoints of the minor axis are (0, (4√11)/7) and (0, -(4√11)/7)
4. **Sketch the ellipse:** 
    * Draw a smooth curve connecting the vertices and the endpoints of the minor axis.

**Key Points:**

* The major axis of the ellipse lies along the x-axis.
* The eccentricity (2/7) indicates that the ellipse is relatively elongated.

I hope this helps! Let me know if you have any other questions.