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

Practice Questions

Q1
What is the focus of the parabola defined by the equation y^2 = 20x?
  1. (5, 0)
  2. (0, 5)
  3. (0, 10)
  4. (10, 0)

Questions & Step-by-Step Solutions

What is the focus of the parabola defined by the equation y^2 = 20x?
  • Step 1: Identify the given equation, which is y^2 = 20x.
  • Step 2: Compare the given equation with the standard form of a parabola, which is y^2 = 4px.
  • Step 3: In the standard form, 4p represents the coefficient of x. Here, we see that 4p = 20.
  • Step 4: To find p, divide both sides of the equation 4p = 20 by 4. This gives p = 20 / 4.
  • Step 5: Calculate p, which equals 5.
  • Step 6: The focus of the parabola is located at the point (p, 0). Since we found p = 5, the focus is at (5, 0).
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