If the parabola `y^(2)=ax` passes through (1, 2) then the equation of the directrix is

Options

A. x+1=0
B. x+2=0
C. x+3=0
D. x+4=0

Answer

To find the equation of the directrix of the parabola given by \( y^2 = ax \) that passes through the point (1, 2), we can follow these steps:

### Step 1: Substitute the point into the parabola's equation
The parabola is given by the equation:
\[ y^2 = ax \]
Since the parabola passes through the point (1, 2), we substitute \( x = 1 \) and \( y = 2 \) into the equation:
\[ 2^2 = a \cdot 1 \]

### Step 2: Solve for \( a \)
Calculating the left side:
\[ 4 = a \]
Thus, we find that:
\[ a = 4 \]

### Step 3: Write the standard form of the parabola
Now, substituting \( a \) back into the equation of the parabola, we have:
\[ y^2 = 4x \]
This matches the standard form of a parabola \( y^2 = 4ax \) where \( a = 1 \).

### Step 4: Find the equation of the directrix
The equation of the directrix for a parabola in the form \( y^2 = 4ax \) is given by:
\[ x = -a \]
Since we found \( a = 4 \), we substitute this value:
\[ x = -4 \]
This can be rewritten as:
\[ x + 4 = 0 \]

### Conclusion
Thus, the equation of the directrix is:
\[ \boxed{x + 4 = 0} \]