Asymptotes of a Hyperbola
Definition. The asymptote of a curve is a straight line approached by the curve line at infinity.
An oblique asymptote is determined by an equation of the form an oblique
To find the slope, we suppose that b=0; then
We find b from the equation .
Passing to the limit, we obtain
Thus, the hyperbola has two asymptotes, passing through the origin:
First, we construct a rectangle with sides 2à along the õ-axis and 2b along the ó-axis. We draw the diagonals in this rectangle and extend them; they are the asymptotes of the hyperbola.
F1 Ì1(–à;0) 0 Ì2(à;0) F2 x
From the vertices M1(–a;0) and M2(a;0), we draw the branches of the hyperbola approaching the asymptotes.
The directrices of a hyperbola. By definition, . By analogy with an ellipse, we find the difference of squares
Date: 2015-01-02; view: 892