Answer: LR = 4.5, e = 5/4.
- A LR = 4.5, e = 5/4
- B LR = 9, e = 4/5
- C LR = 4.5, e = 4/3
- D LR = 9, e = 5/4
Correct answer: A. LR = 4.5, e = 5/4
Explanation: Dividing by 144: x2/16 - y2/9 = 1, so a2=16, b2=9, a=4, b=3. LR = 2b2/a = 2(9)/4 = 4.5. Also c2 = a2+b2 = 25, c=5, so e = c/a = 5/4.
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.