Question 611284
  <pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
Hi,
(x+3)^2+(y+1)^2=4   ||Circle with C(-3,-1) and radius of 2

{{{drawing(300,300,   -6, 6, -6, 6,   grid(1),
circle(-3, -1,0.2),
circle(-3, -1,2.0),
graph( 300, 300, -6, 6, -6, 6))}}}

 (y+2)^2=16px-1)   ||The standard form is {{{(x -h)^2 = 4p(y -k)}}}, where  the focus is (h,k + p)
parabola opening to the right, C(1,-2) and focus(5,-2) 4p=16, p = 4
{{{drawing(300,300,   -6, 6, -6, 6,  blue(line(-5,6,-5,-6))  , grid(1),
circle(1, -2,0.3),
circle(5, -2,0.3),
graph( 300, 300, -6, 6, -6, 6,0, -2+4sqrt(x-1),-2-4sqrt(x-1)))}}}

(x+2)^2/9-(y-3)^2/4=1 
Standard Form of an Equation of an Hyperbola is  {{{(x-h)^2/a^2 - (y-k)^2/b^2 = 1}}} opening right or left
 where Pt(h,k) is a center  with vertices 'a' units right and left of center.
 Asymptotes passing thru the center with slope = ± b/a 
foci being ± sqrt(a^2 + b^2) from center  along axis of symmetry y = b
{{{drawing(300,300,-10,10,-10,10,  grid(1),
circle(-2, 3,0.3),
circle(1, 3,0.3),
circle(-5, 3,0.3),
graph(300,300,-10,10,-10,10,0,3,3+2sqrt(((x+2)^2/9) -1),3-2sqrt(((x+2)^2/9) -1)))}}}
{{{(x-2)^2/2^2+(y+3)^2/3^2=1}}}     ||Ellipse with C(2,-3) V(2,0) and V(2,-6) 
{{{drawing(300,300,   -10,10,-10,10,  arc(2,-3,4,6),
 grid(1),
circle(2, 0,0.4),
circle(2, -6,0.4),
graph( 300, 300, -10,10,-10,10))}}}