Answer: c 2 = a 2 + b 2.
- A c<sup>2</sup> = a<sup>2</sup> - b<sup>2</sup>
- B c<sup>2</sup> = a<sup>2</sup> + b<sup>2</sup>
- C c = a - b
- D c<sup>2</sup> = b<sup>2</sup> - a<sup>2</sup>
Correct answer: B. c<sup>2</sup> = a<sup>2</sup> + b<sup>2</sup>
Explanation: For a hyperbola, c<sup>2</sup> = a<sup>2</sup> + b<sup>2</sup>, 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.