```Question 457306
<pre>
If the equation is

{{{(x-h)^2/a^2 + (y-k)^2/b^2=1}}}

(you can tell which is aČ and which is bČ by the
fact that aČ is always larger than bČ. In this case,
the larger denominator is under the x-term.)

then this is an ellipse shaped like this: &#4363;

The center is (h,k)
The vertices are (h-a,k) and (h+a,k)
The covertices are (h,k-b) and (h,k+b)
The foci are (h-c,k) and (h+c,k),
where c is calculated from {{{c^2=a^2-b^2}}}

-------------------------

If the equation is

{{{(x-h)^2/b^2 + (y-k)^2/a^2=1}}}

(In this case, the larger denominator is under
the y-term.)

then this is an ellipse shaped like this: 0

The center is (h,k)
The vertices are (h,k-a) and (h,k+a)
The covertices are (h-b,k) and (h+b,k)
The foci are (h,k-c) and (h,k+c)
where c is calculated from {{{c^2=a^2-b^2}}}
-------------------------

If the equation is

{{{(x-h)^2/a^2 - (y-k)^2/b^2=1}}}

(In a hyperbola you cannot go by which is larger,
as you can in an ellipse, because with a hyperbola
sometimes a is larger and sometimes b is larger and
sometimes a and b are equal. You have to go by
whether the x term or the y term comes first. aČ will
always be under the first term. In this case the x term
comes first)

Then this is a hyperbola shaped like this: )(

The center is (h,k)
The vertices are (h-a,k) and (h+a,k)
The covertices are (h,k-b) and (h,k+b)
The foci are (h-c,k) and (h+c,k)
where c is calculated from {{{c^2=a^2+b^2}}}

------------------------

If the equation is

{{{(y-k)^2/a^2 - (x-h)^2/b^2=1}}}

(You have to go by whether the x term or the y
term comes first. In this case the y term comes
first)

then this is a hyperbola that opens upward and downward.

The center is (h,k)
The vertices are (h,k-a) and (h,k+a)
The covertices are (h-b,k) and (h+b,k)
The foci are (h,k-c) and (h,k+c)
where c is calculated from {{{c^2=a^2+b^2}}}

-------------------------

Edwin</pre>```