Answer: y2 = 20x.
- A y2 = 5x
- B y2 = 10x
- C y2 = 20x
- D x2 = 20y
Correct answer: C. y2 = 20x
Explanation: Focus (a,0) = (5,0) gives a=5. Equation: y2 = 4ax = 20x.
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.