Answer: y 2 = 8x.
- A y<sup>2</sup> = 8x
- B y<sup>2</sup> = 4x
- C y<sup>2</sup> = 16x
- D y<sup>2</sup> = 2x
Correct answer: A. y<sup>2</sup> = 8x
Explanation: Standard form y²=4ax. Substituting point (2,4): 4²=4a(2) → 16=8a → a=2. So 4a=8. Equation: y²=8x. Verify: (2,4)→16=8(2)=16. ✓ Ans: y²=8x.
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.