What is the location of this parabola's focal point?

y = (1/4)(x – 400)2

Question

What is the location of this parabola's focal point?

y = (1/4)(x – 400)2

dumbcow · Answer

p is distance from vertex to focus
$$p = \frac{1}{4a}$$
where
$$y = a(x-h)^{2} +k$$
so plug in "a" to find "p"
then add that to coord of vertex

anonymous · Answer

but what is a @dumbcow

dumbcow · Answer

its the coefficient in front of (x-400)^2 term
hence the general parabola equation
$$y = a(x-h)^{2} +k$$

anonymous · Answer

y=1/4(x-h)^2+k then?

dumbcow · Answer

no sorry im confusing you ...
im giving the general form...your equation is
$$y = \frac{1}{4}(x-400)^{2}$$
these numbers correspond to coefficient in general form
a = 1/4
h = 400
k=0

anonymous · Answer

Oh okay @dumbcow

anonymous · Answer

I need to have the answer in an ordered pair, though @dumbcow

dumbcow · Answer

focus is always directly above or below the vertex ... if its a function of "x"
so "x-coord" is same as vertex

dumbcow · Answer

vertex: (h,k)

thus

focus: (h, k+p)

anonymous · Answer

@dumbcow thank you

dumbcow · Answer

your welcome