36. The equatiou uz? + 21:1y - by? = 1 represents
(a) a pair of straight line
(b) a conic section with centre at the origin
(c) an ellipse with foci at (1, 0) and (2,0)
(d) a hyperbola with a pair of perpendicular asymptotes
Answers
KEY TAKEAWAYS
Key Points
A conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane; the three types are parabolas, ellipses, and hyperbolas.
A conic section can be graphed on a coordinate plane.
Every conic section has certain features, including at least one focus and directrix. Parabolas have one focus and directrix, while ellipses and hyperbolas have two of each.
A conic section is the set of points
P
whose
distance to the focus is a constant multiple of the distance from
P
to the directrix of the conic.
Key Terms
vertex: An extreme point on a conic section.
asymptote: A straight line which a curve approaches arbitrarily closely as it goes to infinity.
locus: The set of all points whose coordinates satisfy a given equation or condition.
focus: A point used to construct and define a conic section, at which rays reflected from the curve converge (plural: foci).
nappe: One half of a double cone.
conic section: Any curve formed by the intersection of a plane with a cone of two nappes.
directrix: A line used to construct and define a conic section; a parabola has one directrix; ellipses and hyperbolas have two (plural: directrices).
Defining Conic Sections
A conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic sections are the hyperbola, the parabola, and the ellipse. The circle is type of ellipse, and is sometimes considered to be a fourth type of conic section.