Question

Find the equation of the directrix of the parabola x² = 6y ?
1. y = 3/2
2. y = -2/3
3. y = -3/2
4. y = 2/3
5. None of these

Answer 1

Correct Answer - Option 3 : y = -3/2

CONCEPT:

The following are the properties of a parabola of the form: x2 = 4ay where a > 0

• Focus is given by (0, a)
• Vertex is given by (0, 0)
• Equation of directrix is given by: y = - a
• Equation of axis is given by: x = 0
• Length of latus rectum is given by: 4a
• Equation of latus rectum is given by: y = a

CALCULATION:

Given: Equation of parabola is x2 = 6y

The given equation of parabola can be re-written as: x2 = 4 ⋅ (3/2)y       --------(1)

Now by comparing the equation (1) with x2 = 4ay we get

⇒ a = 3/2

As we know that, the equation of directrix of the parabola of the form x2 = 4ay is given by: y = - a

So, the equation of directrix of the given parabola is: y = - 3/2

Hence, option C is the correct answer.