Answer: c2 = a2 + b2.
- A c2 = a2 - b2
- B c2 = a2 + b2
- C c = a - b
- D c2 = b2 - a2
Correct answer: B. c2 = a2 + b2
Explanation: For a hyperbola, c2 = a2 + b2, since the foci lie outside the curve's vertices, making c always greater than a.
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.