8.1.notebook
March 09, 2011
8.1 Conic Sections and Parabolas
A conic section (or conic) is the intersection of a plane and a doublenapped cone.
circle
parabola
elllipse
hyperbola
We should know the equation for a circle already as:
(x - h)2 + (y - k)2 = r2
where (h, k) is the center and r is the radius.
We're changing our thinking about parabolas. We are now focusing on
the curve and getting the equation instead of focusing on the equation
and drawing the curve.
Parabola - The set of all points (x, y) that are equidistant from a fixed
line (directrix) and a fixed point (focus) not on the line.
The midpoint between the focus and the directrix is called the vertex.
The line passing through the focus and the directrix is called the axis.
The axis and the directrix are perpendicular.
8.1.notebook
March 09, 2011
The standard form of the equation of a parabola with vertex at
(h, k) is
(x - h)2 = 4p(y - k)
(up and down)
2
(y - k) = 4p(x - h)
(left and right)
p = the directed distance from the vertex to the focus
4p = focal width
8.1.notebook
March 09, 2011
Ex.) Find the standard form of the equation of the parabola with
vertex (2, 1) and focus (2, 4).
8.1.notebook
March 09, 2011
8.1.notebook
March 09, 2011
p. 641 #2-30 even