Answer: 6.
- A 5
- B 6
- C 8
- D 10
Correct answer: B. 6
Explanation: For the ellipse: e=c/a=3/5, a=10. So c=(3/5)×10=6. Both conics share the same foci, so the common focal distance is c=6. Verify: hyperbola e=c/a<sub>h</sub>=5/3 → a<sub>h</sub>=c×3/5=18/5. Ans: c=6.
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.