COPYRIGHT NOTICE
Copyright 2007 Samuel Dagan
dagan@post.tau.ac.il
/general/copyright.xhtml
Asymptotes of a hyperbola
Hypebola and asymptotes
The origin of the figure is at (0,0)
©
Samuel Dagan
Hyperbola - asymptotes
a
a
x
y
(x/a)²−(y/b)²
= 1 with a=b is
plotted. The marks on the
axes are at
intervals of a.
By definition the lines
x = ±a√2
intersect the
hyperbola at y = ±b.
As shown now, indeed b=a .
The asymptotes
y = ±x
will be drawn
next.
The asymptotes divide the
plane into four segments.
Only
a pair of opposite
segments contains
the hyperbola.
Next the hyperbola with
b = 2a and its
asymptotes
y = ±2x will be
obtained
by animating b .
Verify the marked value of
b and the
asymptote.
The hyperbola with b = a/2
and asymptotes y = ±x/2
will be obtained similarly.
restart
This control bar:
resize by browser's zoom
The graphics, use the mouse:
drag to pan and wheel to zoom
ani-
mate
pause
resume
fast
slow
pause
fast
slow
next
next
end