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What is the length of the latus rectum of the parabola y^2 = 8x?

Practice Questions

Q1
What is the length of the latus rectum of the parabola y^2 = 8x?
  1. 4
  2. 8
  3. 2
  4. 16

Questions & Step-by-Step Solutions

What is the length of the latus rectum of the parabola y^2 = 8x?
  • Step 1: Identify the standard form of the parabola. The equation y^2 = 8x is in the standard 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 of the equation by 4. So, p = 8 / 4 = 2.
  • Step 4: The length of the latus rectum of a parabola is given by the formula 4p.
  • Step 5: Substitute the value of p into the formula. So, the length of the latus rectum = 4 * 2 = 8.
  • Step 6: Conclude that the length of the latus rectum of the parabola y^2 = 8x is 8.
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