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What is the directrix of the parabola defined by the equation y^2 = 20x?

Practice Questions

Q1
What is the directrix of the parabola defined by the equation y^2 = 20x?
  1. x = -5
  2. x = 5
  3. y = 5
  4. y = -5

Questions & Step-by-Step Solutions

What is the directrix of the parabola defined by the equation y^2 = 20x?
  • Step 1: Identify the standard form of a parabola that opens to the right, which is y^2 = 4px.
  • Step 2: Compare the given equation y^2 = 20x with the standard form y^2 = 4px.
  • Step 3: From the equation y^2 = 20x, we can see that 4p = 20.
  • Step 4: Solve for p by dividing both sides of the equation by 4: p = 20 / 4 = 5.
  • Step 5: The directrix of a parabola is given by the equation x = -p.
  • Step 6: Substitute the value of p into the directrix equation: x = -5.
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