<PRE><B>Question 194051</B>
4x^2 + 16x      +y^2 -6y    =  -21
,
if  we  complete  the  squares,  we  can  see  form  
,
4 (x^2 +4x +4)    +y^2 -6y  +9  =  -21  +16  +9,,,,(4*4=16)
,,,,
remember  (4/2)^2 = 4  and   (-6/2)^2  =9,,,,   and  add to  both  sides  to  balance
,
4(x+2)^2  +  (y-3)^2  = 4
,
divide  thru  by  4
,
((x+2)^2)/1 +(  (y-3)^2 )/4=4/4=1
,
the  form for  ellipse  is,  x^2/a^2  +y^2/b^2  =1
therefore  it  fits  an  ellipse</PRE>