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Reviewed CSCA Mathematics question · Hard

A parabola opens to the left and has its vertex at the origin. Its focus is at (-3, 0). What is the equation of the directrix of this parabola?

  1. x = 3
  2. x = -3
  3. y = 3
  4. y = -3
Show the answer and explanation

Correct answer

A. x = 3

Principle or equation

For a parabola with vertex at the origin and focus at (-p, 0) (p > 0), the parabola opens to the left, the equation is y^2 = -4px, and the directrix is the vertical line x = p.

Why this answer is correct

The focus is (-3, 0), so p = 3. The directrix is the vertical line x = p, which is x = 3.

Example

If the focus were (-5, 0), the directrix would be x = 5.

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