Question 440689
  <pre><font face = "Tohoma" size = 4 color = "indigo"><b> 
Hi

a. Find the co-ordinates of the vertex and the focus of the parabola 
 x2=4(x+y)
 x^2 - 4x = 4y
 (x-2)^2 - 4 = 4y  OR (x-2)^2 = 4(y+1)
Using the vertex form of a parabola, {{{y=a(x-h)^2 +k}}} where(h,k) is the vertex
 1/4(x-2)^2 - 1 = y   Vertex (2,-1)
 The standard form is {{{(x -h)^2 = 4p(y -k)}}}, where  the focus is (h,k + p) 
                        (x-2)^2 = 4(y+1)  4p = 4 , p = 1 focus(2,0)

{{{drawing(300,300,   -6, 6, -6, 6,  blue(line(2,6,2,-6))  , grid(1),
circle(2, -1,0.3),
circle(2, 0,0.3),
graph( 300, 300, -6, 6, -6, 6,0, .25(x-2)^2-1))}}}