Correct Answer - Option 4 : All of the above
For a parabola of the form y2 = - 4ax where a > 0 we have:
- Focus is given by: (- a, 0)
- Vertex is given by: (0, 0)
- Equation of directrix is given by: x - a = 0
- Equation of axis is given by: y = 0
- Equation of latus rectum is given by: x + a = 0
- Length of latus rectum is given by: 4a
Given: Equation of parabola is : y2 = - 12x
We can re-write the equation of given parabola as:
⇒ y2 = - 4 ⋅ (3) ⋅ x
Now by comparing the above equation with y2 = - 4ax where a > 0 we get: a = 3.
So, equation of directrix is: x - 3 = 0
Similarly, equation of axis is: y = 0 and equation of latus rectum is: x + 3 = 0.
Hence, option D is true.