Answer:
y=1/2(x-6)^2+3/2
Step-by-step explanation:
General equation of parabola centered at (h,k) and axis of symmetry is parallel to y-axis is given as
(x-h)^2=4p(y-k)^2
where
vertex is at (h,k)
p shows the distance of focus from vertex, f = (h, k + p)
and directrix is given at y = k - p
if value of p is >0 then the focus is above vertex
if value of p<0 then focus is below vertex
Given:
focus= (6,2)
directrix y=1
Comparing above with standard formula of parabola, we get
Also distance p is half the distance from the (6,2) to the directix y=1 which is
1/2=p
As p>0, that means given parabola focus lies above vertex
hence parabola opens upwards
Finding vertex of parabola:
As focus is is at (6,2) and also 1/2 above the vertex so we get vertex at
V=(6,2-1/2)
V=(6,1.5)
Now by comparing above with the standard formula of parabola we have
h=6, k=1.5
Putting values in the formula we get
(x-6)^2=4(1/2)(y-1.5)
(x-6)^2=2(y-1.5)
(x-6)^2=2y-3
Or by re-arranging the terms equation can also be written as
f(x)=1/2(x-6)^2+3/2 !
