Write an equation for the parabola with focus (4,0) and directrix y=2?

Question

I have a hard time writing equations. Can someone give me a very detailed answer?Any help is very much appreciated!

Answer 1

The general formula for a parabola is
4c(y - k) = (x - h)^2
where (h, k) is the vertex.
The focus is (h, k+c)
the directrix is y = k - c
-----------------------------------------
Our focus is (4, 0)
(h, k+c) is the general form, so h = 4 and
k + c = 0
We'll come back to this in a minute...

Our directrix is y = 2
y = k - c is the general form, so
k - c = 2

Now we have two equations and two unknowns...
k + c = 0
k - c = 2
We need to solve those together to find k and c.
k + c = 0
so, k = -c
put that in the other equation...
k - c = 2
(-c) - c = 2
-2c = 2
c = -1
put that in the first equation...
k = -c
k = -(-1) = 1

Now we know h = 4, k = 1, and c = -1. Just put those into the general parabola equation...

4c(y - k) = (x - h)^2
4(-1)(y - 1) = (x - 4)^2
-4y + 4 = (x - 4)^2
-4y = (x - 4)^2 - 4
y = (-1/4)(x - 4)^2 + 1
(That is the standard form of the parabola equation.)

Answer 2

if y= 2
then the genral equation of parabola is
x square = -4ay
since focus is 4,0 then a = 4
the equation of parabola is
x square = -4*4 y
x square = -16y

Answer 3

there is something wrong with this
as the focus implies that the parabola has
the form: y^2=4ax
but the derectix implies that the parabola
has the form x^2=4ax