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<sup>2</sup> = b<sup>2</sup> - a<sup>2</sup>
- D c = a + b
Correct answer: B. c<sup>2</sup> = a<sup>2</sup> - b<sup>2</sup>
Explanation: For an ellipse, c<sup>2</sup> = a<sup>2</sup> - b<sup>2</sup>, since the foci lie inside the ellipse.
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.