Answer: y = ±(3/4)x.
- A y = ±(4/3)x
- B y = ±(3/4)x
- C y = ±(9/16)x
- D y = ±(16/9)x
Correct answer: B. y = ±(3/4)x
Explanation: Asymptotes of x<sup>2</sup>/a<sup>2</sup> - y<sup>2</sup>/b<sup>2</sup> = 1 are y = ±(b/a)x = ±(3/4)x since a=4, b=3.
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.