Directrix and Focus

Dirac

vertex (-2, 3), focus (0,3)

Find the equation of the parabola.

Dirac.

lurflurf

What have you tried so far?
Find the directix. then recall
A parabola is the set of point equidistant from the focus and directix.

Dirac

So far I have got to this

((y-3)^2)=4a(x+2)

What now

Dirac.

lurflurf

a will be the distance between the focus and vertex.
Why is this?

Dirac

How does one find the vertex

lurflurf

you started out with
vertex (-2, 3), focus (0,3)
The points of a parabola are equidistant from it directrix and focus.
The vertex is the point closest to them. that is
distance(vertex,focus)<=distance(point on parabola,focus)
with equality only when the point is the vertex.

Dirac

Could you just post the answer, or would it get up your backside to post something useful in your life

Dirac.

lurflurf

I already said you a is the distance between
vertex (-2, 3), focus (0,3)
here you go
a=sqrt[(0-(-2))^2+(3-3)]
=sqrt[2^2]
a=2
Do you understand why?
Can you find the equation of a parabola with
vertex (0,0), focus (0,-4)

HallsofIvy

How pathetic. Why in the world would anyone care what the answer to some made up question like this is? The whole point of an exercise like this is to learn how to get the answer. I'll bet there's a "general formula" for the parabola in the same section of your text as this problem. Look it up. We're here for people who want to learn not for people who want the answers handed to them.