# Directrix and Focus

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

Find the equation of the parabola.

Dirac.

lurflurf
Homework Helper
Dirac said:
vertex (-2, 3), focus (0,3)

Find the equation of the parabola.

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

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

So far I have got to this

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

What now

Dirac.

lurflurf
Homework Helper
Dirac said:
So far I have got to this

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

What now

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

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

How does one find the vertex

lurflurf
Homework Helper
Dirac said:
How does one find the vertex
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.

lurflurf said:
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.

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

Dirac.

lurflurf
Homework Helper
Dirac said:
Could you just post the answer, or would it get up your backside to post something useful in your life

Dirac.
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