Which of the following is/are true ?
The circle `x^(2)+y^(2)-6x+6y+9=0` and the axes are such that :

Options

A. They do not intersect
B. They touch each other
C. Their exterior common tangents are parallel
D. Their interior common tangents are perpendicular

Answer

To solve the problem, we need to analyze the given equation of the circle and determine its properties in relation to the axes.

### Step-by-step Solution:

1. **Write the equation of the circle:**
The given equation is:
\[ x^2 + y^2 - 6x + 6y + 9 = 0 \]

2. **Rearrange the equation:**
We can rearrange the equation to group the \(x\) and \(y\) terms:
\[ x^2 - 6x + y^2 + 6y + 9 = 0 \]

3. **Complete the square for \(x\) and \(y\):**
- For \(x\):
\[ x^2 - 6x = (x - 3)^2 - 9 \]
- For \(y\):
\[ y^2 + 6y = (y + 3)^2 - 9 \]

Substituting these back into the equation gives:
\[ (x - 3)^2 - 9 + (y + 3)^2 - 9 + 9 = 0 \]
Simplifying this results in:
\[ (x - 3)^2 + (y + 3)^2 - 9 = 0 \]
Which can be rewritten as:
\[ (x - 3)^2 + (y + 3)^2 = 9 \]

4. **Identify the center and radius of the circle:**
From the equation \((x - 3)^2 + (y + 3)^2 = 9\):
- The center of the circle is at \((3, -3)\).
- The radius \(r\) is \(\sqrt{9} = 3\).

5. **Determine the distance from the center to the axes:**
The distance from the center \((3, -3)\) to the x-axis is \(3\) units (the y-coordinate) and to the y-axis is also \(3\) units (the x-coordinate).

6. **Analyze the relationship between the circle and the axes:**
Since the radius of the circle is \(3\) and the distances from the center to both axes are also \(3\), the circle will touch both axes at the points \((3, 0)\) and \((0, -3)\).

7. **Conclusion about the axes and the circle:**
- The axes do not intersect the circle; they touch it at exactly one point each.
- The internal tangents to the circle from the axes are perpendicular to each other.

### Final Answer:
Based on the analysis, the correct options are:
- The axes do not intersect the circle.
- The axes touch the circle.
- The internal common tangents are perpendicular.