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The given equation in polar coordinates is \( r = 6 \). To convert this to rectangular (or Cartesian) coordinates, we use the relationships between polar and rectangular coordinates:

- \( x = r \cos(\theta) \)
- \( y = r \sin(\theta) \)
- \( r^2 = x^2 + y^2 \)

Since \( r = 6 \), we can square both sides:

\[
r^2 = 6^2 = 36
\]

Now, substitute \( r^2 \) with \( x^2 + y^2 \):

\[
x^2 + y^2 = 36
\]

This is the equation of a circle with radius 6 and centered at the origin in rectangular coordinates.

Would you like more details or clarification on any steps?

Here are 5 follow-up questions to expand on this:
1. What are polar coordinates, and how are they different from rectangular coordinates?
2. How would you convert an equation in rectangular coordinates back into polar form?
3. What does the equation \( r = 6 \) represent geometrically in polar coordinates?
4. How would the equation change if the center of the circle was shifted to another point?
5. What other geometric shapes can be represented using polar coordinates?

**Tip:** In polar coordinates, the angle \( \theta \) can give additional information about the direction of a point, while \( r \) represents the distance from the origin.

Convert the equation r = 6 to rectangular coordinates and write in standard form.

Convert the polar equation r = 6 to rectangular coordinates using basic geometric relationships. This conversion results in the equation of a circle centered at the origin with radius 6, and is suitable for students in Grades 9-12.

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