15Nov 2014 by Vincent Summers No Comments

Analytic Geometry: The Hyperbola

Mathematics
[caption id="attachment_6399" align="alignright" width="380"] Simple hyperbola with asymptotes. Image by author.[/caption] The parabola, ellipse, circle, and hyperbola are all termed conic sections. This means that a plane that cuts into a cone in just the right way will generate one of these figures. We will consider the basic equation of a hyperbola and graph one. Equation of an Hyperbola It may be recalled the equation for an ellipse centered at the origin is, x2/a2 + y2/b2 = 1 where 2a is the length of the ellipse and 2b is its height. The equation for an hyperbola centered at the origin is very similar, x2/a2 - y2/b2 = 1 The graph of this function is completely different from that of an ellipse. Let's look at a very basic one, for which…
Read More
28Oct 2014 by Vincent Summers No Comments

Analytic Geometry: The Ellipse and the Circle

Mathematics
The circle is really a special type of ellipse. In analytic geometry, an ellipse is a mathematical equation that, when graphed, resembles an egg. An ellipse has two focal points. The distance apart between the two points is one way of describing a particular ellipse. If the two points come together the ellipses become a circle with the point at its center. The equation for an ellipse is, x2/a2 + y2/b2 = 1 In this equation, "a" and "b" are constants that determine the shape of the ellipse, whereas x and y are variables, i.e., they can take on a host of values. When the value for x is known, the value for y is determined. Or, if it is y that is known, then x is determined. If a…
Read More