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Reviewed CSCA Mathematics question · Easy

What is the focus of the parabola given by the equation y^2 = -16x?

  1. (-4, 0)
  2. (4, 0)
  3. (0, -4)
  4. (0, 4)
Show the answer and explanation

Correct answer

A. (-4, 0)

Principle or equation

For a parabola of the form y^2 = 4px, the focus is at (p, 0). If the coefficient is negative, the parabola opens to the left and the focus is at (-p, 0).

Why this answer is correct

The equation y^2 = -16x can be written as y^2 = 4(-4)x, so p = -4. The focus is at (p, 0) = (-4, 0).

Example

For y^2 = 12x, p = 3, focus is (3, 0).

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