Answer: sqrt(3)/2.
- A 1/2
- B sqrt(3)/2
- C 1/sqrt(2)
- D sqrt(2)/3
Correct answer: B. sqrt(3)/2
Explanation: Latus rectum = 2b2/a. Minor axis = 2b. Given 2b2/a = (1/2)(2b) = b, so 2b2/a = b gives 2b = a, b = a/2. Then e2 = 1 - b2/a2 = 1 - 1/4 = 3/4, so e = sqrt(3)/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.