Answer: ±2.
- A ±1
- B ±2
- C ±√2
- D ±4
Correct answer: B. ±2
Explanation: Tangency requires c² = r²(1 + m²) = 2·2 = 4, so c = ±2.
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.