Question

If the equation of parabola is y² = -12x, then which of the following is true ?
1. Equation of axis is: y = 0
2. Equation of directrix is: x - 3 = 0
3. Equation of latus rectum is: x + 3 = 0
4. All of the above
5. None of these

Answer 1

Correct Answer - Option 4 : All of the above

Concept:

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

Calculation:

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.