<s>
In	O
mathematics	O
,	O
a	O
translation	B-Algorithm
of	I-Algorithm
axes	I-Algorithm
in	O
two	O
dimensions	O
is	O
a	O
mapping	B-Algorithm
from	O
an	O
xy-Cartesian	O
coordinate	O
system	O
to	O
an	O
x'y'-Cartesian	O
coordinate	O
system	O
in	O
which	O
the	O
x	O
 '	O
axis	O
is	O
parallel	O
to	O
the	O
x	O
axis	O
and	O
k	O
units	O
away	O
,	O
and	O
the	O
y	O
 '	O
axis	O
is	O
parallel	O
to	O
the	O
y	O
axis	O
and	O
h	O
units	O
away	O
.	O
</s>
<s>
A	O
translation	B-Algorithm
of	I-Algorithm
axes	I-Algorithm
in	O
more	O
than	O
two	O
dimensions	O
is	O
defined	O
similarly	O
.	O
</s>
<s>
A	O
translation	B-Algorithm
of	I-Algorithm
axes	I-Algorithm
is	O
a	O
rigid	B-Algorithm
transformation	I-Algorithm
,	O
but	O
not	O
a	O
linear	B-Architecture
map	I-Architecture
.	O
</s>
<s>
(	O
See	O
Affine	B-Algorithm
transformation	I-Algorithm
.	O
)	O
</s>
<s>
Next	O
,	O
a	O
translation	B-Algorithm
of	I-Algorithm
axes	I-Algorithm
can	O
reduce	O
an	O
equation	O
of	O
the	O
form	O
(	O
)	O
to	O
an	O
equation	O
of	O
the	O
same	O
form	O
but	O
with	O
new	O
variables	O
(	O
x	O
 '	O
,	O
y	O
 '	O
)	O
as	O
coordinates	O
,	O
and	O
with	O
D	O
and	O
E	O
both	O
equal	O
to	O
zero	O
(	O
with	O
certain	O
exceptions	O
—	O
for	O
example	O
,	O
parabolas	O
)	O
.	O
</s>
<s>
In	O
the	O
examples	O
that	O
follow	O
,	O
it	O
is	O
assumed	O
that	O
a	O
rotation	B-Algorithm
of	I-Algorithm
axes	I-Algorithm
has	O
already	O
been	O
performed	O
.	O
</s>
<s>
by	O
using	O
a	O
translation	B-Algorithm
of	I-Algorithm
axes	I-Algorithm
,	O
determine	O
whether	O
the	O
locus	O
of	O
the	O
equation	O
is	O
a	O
parabola	O
,	O
ellipse	O
,	O
or	O
hyperbola	O
.	O
</s>
<s>
Equations	O
(	O
)	O
define	O
a	O
translation	B-Algorithm
of	I-Algorithm
axes	I-Algorithm
in	O
three	O
dimensions	O
where	O
(	O
h	O
,	O
k	O
,	O
l	O
)	O
are	O
the	O
xyz-coordinates	O
of	O
the	O
new	O
origin	O
.	O
</s>
<s>
A	O
translation	B-Algorithm
of	I-Algorithm
axes	I-Algorithm
in	O
any	O
finite	O
number	O
of	O
dimensions	O
is	O
defined	O
similarly	O
.	O
</s>
<s>
As	O
in	O
the	O
case	O
of	O
plane	O
analytic	O
geometry	O
,	O
the	O
method	O
of	O
translation	B-Algorithm
of	I-Algorithm
axes	I-Algorithm
may	O
be	O
used	O
to	O
simplify	O
second-degree	O
equations	O
,	O
thereby	O
making	O
evident	O
the	O
nature	O
of	O
certain	O
quadric	O
surfaces	O
.	O
</s>
