Question 429414
  <pre><font face = "Tohoma" size = 4 color = "indigo"><b>
Hi
11x^2-3y^2-88x+18y+116=0 
11[(x-4)^2-16] -3[(y+3)^2-9] +116=0 
11(x-4)^2-176 -3(y+3)^2+ 27 +116=0
 11(x-4)^2 -3(y+3)^2= 33 
{{{ (x-4)^2/3 -(y+3)^2/11= 1 }}} Hyperbola

 x^2+y^2+8x-4y=-11 
(x+4)^2 -16 + (y-2)^2 - 4 =-11
 {{{(x+4)^2 + (y-2)^2 = 9}}}  |Circle

y^2-4x+6y+24=0 
(y+3)^2 - 9 - 4x +24 = 0
(y+3)^2 = 4x -13   |Parabola
 x = .25(y+3)^2 +13/4   Vertex Pt(13/4,-3)  
{{{drawing(300,300,   -6, 6, -6, 6,  grid(1),
circle(13/4, -3,0.3),
graph( 300, 300, -6, 6, -6, 6,0,2sqrt(4x-13)-3,-2sqrt(4x-13)-3 ))}}}