Find the co-ordinate of focus and the equation of the directrix of the parabola `y^2=4ax`, if it passes through the point(3,-2).

Explanation

To solve the problem of finding the coordinates of the focus and the equation of the directrix of the parabola given by the equation \( y^2 = 4ax \), which passes through the point \( (3, -2) \), we can follow these steps:

### Step 1: Identify the standard form of the parabola
The given equation of the parabola is \( y^2 = 4ax \). In this form, the focus is located at the point \( (a, 0) \) and the equation of the directrix is \( x = -a \).

### Step 2: Substitute the point into the parabola equation
Since the parabola passes through the point \( (3, -2) \), we can substitute \( x = 3 \) and \( y = -2 \) into the equation \( y^2 = 4ax \):
\[
...