The equation $y^2 = 4ax$ is the equation of a parabola in Cartesian coordinates. To convert this into polar coordinates, we use the relationships:

$x = r \cos \theta \quad \text{and} \quad y = r \sin \theta$

Substitute these into the given equation:

$(r \sin \theta)^2 = 4a(r \cos \theta)$

This simplifies to:

$r^2 \sin^2 \theta = 4ar \cos \theta$

Now, divide both sides by $r$ (assuming $r \neq 0$):

$r \sin^2 \theta = 4a \cos \theta$

Therefore, the equation in polar coordinates is:

$r = \frac{4a \cos \theta}{\sin^2 \theta}$

This is the polar form of the parabola $y^2 = 4ax$ with the origin as the pole.

Would you like further details or have any questions?

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Here are 5 related questions:

1. How do you convert a general conic section to polar coordinates?
2. What is the geometric interpretation of this parabola in polar coordinates?
3. How would you find the directrix of the parabola $y^2 = 4ax$ in polar form?
4. What happens to the equation if you move the origin to a different point?
5. How can this transformation help in graphing polar curves?

Tip: Always remember to substitute $x$ and $y$ with $r \cos \theta$ and $r \sin \theta$ respectively when converting between Cartesian and polar coordinates.