Find the vertex, focus, length of the latus rectum , equation of directrix of the parabola `3y^2=5x`.

Explanation

To solve the problem of finding the vertex, focus, length of the latus rectum, and the equation of the directrix of the parabola given by the equation \(3y^2 = 5x\), we will follow these steps:

### Step 1: Rewrite the equation in standard form
The given equation is \(3y^2 = 5x\). We can rewrite this in the standard form of a parabola.

To do this, we divide both sides by 3:
\[
y^2 = \frac{5}{3}x
...