Question

For the parabola \( y^2 = -12x \), the equation of the directrix is  \( x = a \). The value of  \( a \) is:

• A. 3
• B. 4
• C. 2
• D. 6

Hint:

For parabolas of the form \( y^2 = 4ax \), the directrix is given by \( x = -a \).

Answer 1

The Correct Option is A

Step 1: The standard form of the equation of a parabola is \( y^2 = 4ax \). For the given equation \( y^2 = -12x \), we compare it with the standard form: \[ y^2 = 4ax \quad \Rightarrow \quad 4a = -12 \quad \Rightarrow \quad a = -3. \] Step 2: The equation of the directrix for a parabola is given by \( x = -a \). Since \( a = -3 \), the equation of the directrix is: \[ x = 3. \] Thus, the value of \( a \) is 3.