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The equation of the directrix of the parabola y^2 = 8x is?

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Question: The equation of the directrix of the parabola y^2 = 8x is?

Options:

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

Correct Answer: x = -2

Solution: 

The directrix of the parabola y^2 = 8x is given by x = -2.

The equation of the directrix of the parabola y^2 = 8x is?

Practice Questions

Q1
The equation of the directrix of the parabola y^2 = 8x is?
  1. x = -2
  2. x = 2
  3. y = -4
  4. y = 4

Questions & Step-by-Step Solutions

The equation of the directrix of the parabola y^2 = 8x is?
  • Step 1: Identify the standard form of the parabola. The equation y^2 = 8x is in the form y^2 = 4px.
  • Step 2: Compare the given equation with the standard form. Here, 4p = 8.
  • Step 3: Solve for p by dividing both sides by 4. So, p = 8 / 4 = 2.
  • Step 4: Understand that for a parabola that opens to the right, the directrix is given by the equation x = -p.
  • Step 5: Substitute the value of p into the directrix equation. So, x = -2.
  • Parabola Properties – Understanding the standard form of a parabola and its geometric properties, including the focus and directrix.
  • Directrix Calculation – Knowing how to derive the equation of the directrix from the standard form of a parabola.
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