Question 618492
  <pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
Hi,
How do you write the equation of the indicated conic in standard form? 
Parabola: Vertex:(2,8) Directrix:Y =4   Opens Upward 
The standard form is {{{(x -h)^2 = 4p(y -k)}}}, where  the focus is (h,k + p) 
(x-2)^2 = 4p(y -8)  p = 4, 4p = 16
 {{{y = highlight(1/16)(x-2)^2 + 8}}}
Hyperbola: Vertices:(-3,2),(7,2) Foci:(-5,2),(9,2) Opening Right and Left along y =2  C(2,2), a = 5
 {{{(x-2)^2/5^2 - (y-2)^2/b^2 = 1}}}
Foci:(-5,2),(9,2)  f = 7 = sqrt(25 + b^2), b = sqrt(24)
{{{(x-2)^2/25 - (y-2)^2/24 = 1}}}
{{{drawing(300,300,   -10,10,-10,10,  
 grid(1),
circle(2, 8,0.4),

graph( 300, 300, -10,10,-10,10,0,4,2 (1/16 )(x-2)^2 + 8))}}}