Question 448900
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Hi
5. ellipse with center at (0,0) vertex (-4,0) and co-vertex (0,3) 
   {{{x^2/16 + y^2/9 = 1}}}
6. circle with center at (-1,2) and radius 4.  {{{(x+1)^2 + (y-2)^2 = 16}}}
7. parabola with vertex at (0,0) and directrix x = -3 
      y^2 = (3/4)x    4p = 3     p = 3/4
8. hyperbola with foci at (-3,0) and (3,0) and vertices at (2,0) and (-2,0)
  y^2/4 - x^2/5 = 1    c ={{{sqrt(4 + a^2)}}} = 3   a = {{{sqrt(5)}}}

{{{drawing(300,300,  -10,10,-10,10, grid(1),arc(0,0,8,6),blue(line(-3,10,-3,-10)),  
circle(-1, 2,0.3),
circle(-1, 2,4),
circle(3, 0,0.3),
circle(-3, 0,0.3),
graph( 300, 300,-10,10,-10,10,2sqrt((x)^2/5 + 1),-2sqrt((x)^2/5 +1), sqrt((4/3)x), -sqrt((4/3)x)))}}}
Standard Form of an Equation of a Circle is {{{(x-h)^2 + (y-k)^2 = r^2}}} 
where Pt(h,k) is the center and r is the radius

 Standard Form of an Equation of an Ellipse is {{{(x-h)^2/a^2 + (y-k)^2/b^2 = 1 }}}
where Pt(h,k) is the center and a and b  are the respective vertices distances from center.

Standard Form of an Equation of an Hyperbola is  {{{(x-h)^2/a^2 - (y-k)^2/b^2 = 1}}} where Pt(h,k) is a center  with vertices 'a' units right and left of center.
Standard Form of an Equation of an Hyperbola opening up and down is:
  {{{(y-k)^2/b^2 - (x-h)^2/a^2 = 1}}} where Pt(h,k) is a center  with vertices 'b' units up and down from center.

Using the vertex form of a parabola, {{{y=a(x-h)^2 +k}}} where(h,k) is the vertex
 The standard form is {{{(x -h)^2 = 4p(y -k)}}}, where  the focus is (h,k + p)