Conics There are four
conic sections which are often discussed in algebra classes, these include: the parabola, the circle, the ellipse, and the hyperbola.
Given an equation, you should be able to determine which of the four conic
sections the equation represents. It is fairly easy to determine the
type of conic section from the equation. The parabola is an equation
in two variables (usually x and y) where _{} and _{} are equations whose graphs would be parabolas. For the
circle, the ellipse, and the hyperbola
both the x . These conics can best be
distinguished by observing the coefficients of the equation in the form
. If a = b, then the graph of the equation would be a
circle. For example, is an equation whose graph would be a circle. If a
≠ b, but both a and b have the same sign, then the graph of the equation
would be an ellipse. For example,
and are equations whose graphs would be ellipses. Finally,
if a and b have different signs, then the graph of the equation would be a
hyperbola. For example, and are equations whose graphs would be hyperbolas. Once
again, I am limited to using FrontPage to create this review; therefore, I
cannot show examples of the graphs. However, I can give you a few
pointers on the graphs.
the y variables are squared termsandThe The graphing form for the is
. To transform the ellipse
from the standard form to the graphing form, divide all
terms by the constant number …
and .ellipseOnce this is accomplished, the a will designate the
x-intercepts and the b will designate the y-intercepts of the ellipse
“centered” at (0,0). Thus, the x-intercepts are at ±2 and the
y-intercepts are at .
The views and
opinions expressed in this page are strictly those of Mary Lou Baker. This page was edited on 19-Sep-2007 |