Question

Find the equation of the parabola with focus (5, 1) and directrix y = -1.

Answer 1

ok there you are
first lets draw a picture so we see what it looks like kinda

Answer 2

ok .

Answer 3

the vertex is half way between the focus and the directrix
that means it is at \((5,0)\)
also we see it opens up, so the \(x\) term will be squared not the \(y\) term

Answer 4

general form is \[4p(y-k)=(x-h)^2\] in your case \(h=5,k=0\)

Answer 5

\(p\) is the distance between the focus and the vertex, which is 1
so it is
\[4y=(x-5)^2\] done

Answer 6

if you have multiple choice problem and don't see that answer, i could be written as
\[y=\frac{1}{4}(x-5)^2\] we can check it if you like

Answer 7

my choices are :
(x-5)^2 = 4y
(y-5)^2 = 4x
(x-5)^2 = -4y
(y-5)^2 = -4x

Answer 8

\[4y=(x-5)^2\] is the same as \[(x-5)^2=4y\]right?

Answer 9

yes because a+z = z+a i think .

Answer 10

can you help me with another one ?

Answer 11

@satellite73

Answer 12

sure post again