The focus of the parabola `y^(2) = - `4ax is :

Options

A. (2, a)
B. (-a, 0)
C. (0,2)
D. (0, -2)

Answer

To find the focus of the parabola given by the equation \( y^2 = -4ax \), we can follow these steps:

### Step 1: Identify the standard form of the parabola
The equation \( y^2 = -4ax \) is in the standard form of a parabola that opens to the left. The general form for a leftward-opening parabola is given by:
\[ y^2 = -4px \]
where \( p \) is the distance from the vertex to the focus.

### Step 2: Determine the vertex
For the parabola \( y^2 = -4ax \), the vertex is at the origin (0, 0).

### Step 3: Identify the value of \( p \)
In our case, comparing \( y^2 = -4ax \) with \( y^2 = -4px \), we can see that:
\[ 4p = 4a \implies p = a \]

### Step 4: Locate the focus
Since the parabola opens to the left, the focus will be located at a distance \( p \) (which is \( a \)) to the left of the vertex. Therefore, the coordinates of the focus will be:
\[ (-p, 0) = (-a, 0) \]

### Conclusion
Thus, the focus of the parabola \( y^2 = -4ax \) is at the point:
\[ \text{Focus} = (-a, 0) \]