Question

Find the equation of the directrix of the parabola x² = 64y
1. y = 16
2. x = 16
3. y = - 16
4. x = -16

Answer 1

Correct Answer - Option 3 : y = - 16

Concept:

Parabola:

The equation of directrix of the parabola x2 = 4ay is given by: y = - a

Calculation:

Given: x2 = 64y

The given equation can be written as, x² = 4 ⋅ 16 ⋅ y

By comparing the above equation with the standard equation of the parabola, x2 = 4ay we get

⇒ a = 16

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

⇒ y = - 16

Hence, the correct option is 3.