Answer:
(x+2)²=4(y-4)
or y=1/4 (x+2)²+4
Step-by-step explanation:
directrix y=3 and focus (-2,5) to find te equation of parabola we use the equation :
(x-h)²=4p(y-k)
vertex(h,k) : the vertex is half way between the focus and the directrix
y(vertex)=y(focus)+directrix/2
y=5+3/2 ⇒8/2=4
x is the same as the c of the focus =-2
vertex (-2,4)
to find the distance (p) which is the distance between the vertex and focus
p=5-4=1
substitute h=(-2), k=(4) and p=(1) in the equation : (x-h)²=4p(y-k)
(x-(-2)²=4(1)(y-4)
(x+2)²=4(y-4)
