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The problem asks to convert the given equations from Cartesian coordinates to polar coordinates. 

In polar coordinates, the relationships between Cartesian coordinates \((x, y)\) and polar coordinates \((r, \theta)\) are as follows:
- \(x = r \cos \theta\)
- \(y = r \sin \theta\)
- \(r^2 = x^2 + y^2\)

Let’s solve each equation:

### (a) \(y = 6\)
We substitute \(y = r \sin \theta\):
\[
r \sin \theta = 6
\]
Thus, the equation in polar coordinates is:
\[
r = \frac{6}{\sin \theta}
\]
or:
\[
r = 6 \csc \theta
\]

### (b) \(y^2 = 8x\)
We substitute \(y = r \sin \theta\) and \(x = r \cos \theta\):
\[
(r \sin \theta)^2 = 8 (r \cos \theta)
\]
Simplifying:
\[
r^2 \sin^2 \theta = 8r \cos \theta
\]
If \(r \neq 0\), we can divide both sides by \(r\):
\[
r \sin^2 \theta = 8 \cos \theta
\]
Thus, the equation in polar coordinates is:
\[
r = \frac{8 \cos \theta}{\sin^2 \theta}
\]
or equivalently:
\[
r = 8 \cot \theta \csc \theta
\]

Let me know if you need further clarification on any step.

Here are some related questions to explore:
1. How do you derive the relationship between Cartesian and polar coordinates?
2. What happens if \(\theta = 0\) or \(\theta = \pi/2\) in these equations?
3. Can you convert \(r = 6 \csc \theta\) back to Cartesian coordinates?
4. How do polar coordinates simplify the equation of a circle?
5. How do you convert polar equations back to Cartesian form?

**Tip:** When converting equations, remember that \(r\) must always be non-negative, and \(\theta\) typically lies in the interval \([0, 2\pi)\).

Ubahlah ke sistem koordinat kutub, persamaan: a. y = 6 b. y^2 = 8x

Learn how to convert the Cartesian equations y = 6 and y^2 = 8x to polar coordinates. This problem involves key concepts like coordinate geometry and the conversion between Cartesian and polar forms using specific formulas. Suitable for students in Grades 10-12.

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