Can someone also tell me What are (a) the x-intercepts, 
(b) the y-intercepts and (c) the foci of the ellipse
 
(a)_________
(b)_________
(c)_________

Principles you need to learn about the two forms of ellipses.

What is important at first is to observe whether the number
underneath the x² is greater than or less than the number
undernesth the y².  The larger of these is always a² amd the
smaller one is always b². 

Rule 1.

  where 

represents an ellipse that looks like this ( 
without the pointy thingy.

x-intercepts (a,0) and (-a,0) 
y-intercepts (0,b) and (0,-b)

Now to find the foci, first you must
calculate c by the formula

 = ±

for the x-values of the foci.

So the foci are (-c,0) and (c,0).

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

Rule 2.

  where 

represents an ellipse that is shaped like a zero 0 

x-intercepts (b,0) and (-b,0) 
y-intercepts (0,a) and (0,-a)

Now to find the foci, first you must
calculate c by the formula

 = ±

for the x-values of the foci.

So the foci are (0,c) and (0,-c).

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

Yours here is the second case since the number
under the y² is greater than the number under 
the x²:



so we use rule 2.

 so 

 so 


  since 

represents an ellipse that is shaped like a zero 0 

x-intercepts (5,0) and (-5,0) 
y-intercepts (0,6) and (0,-6)

Now to find the foci, first you must
calculate c by the formula

 = ± = ± = ±

or about ±3.3

for the x-values of the foci.

So the foci are (0,) and (0,),
or about (0,3.3) and (0,-3.3)
 
  
Here's the graph. The foci are marked with little short lines:

Edwin