Answer: (3, 0).
- A (3, 0)
- B (6, 0)
- C (12, 0)
- D (0, 3)
Correct answer: A. (3, 0)
Explanation: Comparing with y<sup>2</sup> = 4ax gives 4a = 12, so a = 3. The focus is (a, 0) = (3, 0).
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.