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The problem asks for the equation of an ellipse, centered at \((-2, 1)\), with one focus at \((-6, 1)\), and a minor axis length of 6 units.

### Step 1: Recognize the general form of the ellipse equation
For an ellipse centered at \((h, k)\), the equation is:

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

where:
- \( (h, k) \) is the center,
- \(a\) is the semi-major axis (half the length of the major axis),
- \(b\) is the semi-minor axis (half the length of the minor axis).

### Step 2: Find the center and minor axis
The center is given as \((-2, 1)\), so \( h = -2 \) and \( k = 1 \).

The minor axis length is 6, meaning the semi-minor axis \( b = \frac{6}{2} = 3 \). Hence, \( b^2 = 9 \).

### Step 3: Determine the distance between the foci
The distance between the center \((-2, 1)\) and the focus \((-6, 1)\) is the value of \( c \). The formula for this distance is:

\[
c = \sqrt{(h - x_f)^2 + (k - y_f)^2}
\]

Substitute \((-2, 1)\) for \((h, k)\) and \((-6, 1)\) for the focus \((x_f, y_f)\):

\[
c = \sqrt{(-2 - (-6))^2 + (1 - 1)^2} = \sqrt{(-2 + 6)^2} = \sqrt{4^2} = 4
\]

Thus, \( c = 4 \).

### Step 4: Relate the values using the ellipse formula
For an ellipse, the relationship between \(a\), \(b\), and \(c\) is:

\[
c^2 = a^2 - b^2
\]

Substitute \( c = 4 \) and \( b^2 = 9 \):

\[
16 = a^2 - 9 \implies a^2 = 25
\]

Thus, \( a = 5 \).

### Step 5: Write the equation of the ellipse
Now that we have \( h = -2 \), \( k = 1 \), \( a^2 = 25 \), and \( b^2 = 9 \), we can substitute these values into the general equation of the ellipse:

\[
\frac{(x + 2)^2}{25} + \frac{(y - 1)^2}{9} = 1
\]

This is the equation of the ellipse.

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### Related Questions:
1. How do you find the foci of an ellipse given its equation?
2. What is the geometric meaning of the minor axis in an ellipse?
3. How can you determine the orientation of the ellipse based on its equation?
4. Can the ellipse ever become a circle? If so, under what conditions?
5. How does changing the values of \(a\) and \(b\) affect the shape of the ellipse?

### Tip:
In ellipses, the relationship \(c^2 = a^2 - b^2\) holds true for all ellipses, where \(a\) is the semi-major axis and \(b\) is the semi-minor axis. It’s important to carefully distinguish these when solving problems.

Persamaan elips yang berpusat di (-2, 1) dengan salah satu titik fokus di (-6, 1) dan panjang sumbu minornya 6 satuan adalah ....

Solve the equation of an ellipse centered at (-2, 1), with a focus at (-6, 1) and a minor axis length of 6 units. This problem involves using the standard equation of an ellipse, distance formula, and the Pythagorean relationship in ellipses.

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