Find the equation of the directrix and axis of the parabola x2 = - 16y

  1. x = - 4 and y = 0
  2. y = - 4 and x = 0
  3. x = 4 and y = 0
  4. y = 4 and x = 0

Answer (Detailed Solution Below)

Option 4 : y = 4 and x = 0
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Detailed Solution

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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 = - 16y

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

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

⇒ a = 4

As we know that, 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 = 4

As we know that, equation of axis of the parabola of the form x2 = - 4ay is given by: x = 0

Hence, option D is the correct answer.

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