Answer: x = -3.
- A x = -3
- B x = 3
- C x = -6
- D y = -3
Correct answer: A. x = -3
Explanation: Since 4a = 12, a = 3. The directrix of y<sup>2</sup> = 4ax is x = -a, so x = -3.
All four conics form a single family distinguished only by eccentricity: a circle is the most "closed" (e=0), an ellipse is an elongated closed curve, a parabola is the borderline open curve (e=1), and a hyperbola has two separate open branches (e>1).
Concept context
Study circles, parabolas, ellipses, and hyperbolas as curves formed by intersecting a plane with a double cone, with their standard equations and key properties.