There are 2 answers, because the parabola can open right or
it can open left.
The equation of a parabola that faces left or right is
Where (h,k) is the vertex
If p is taken positive it opens to the right, if
p is taken negative, it opens to the left.
The latus rectum is 4p. That's the green line, which
is 6 units in length. I'll just do the one that opens
to the right. So 4p = +6, taking it positive.
p =
The distance p is the distance from the vertex to the
focus. So the vertex of the first parabola is
or units left of the focus (-2,-1), and
that point is
(h,k) =
So the equation of the first parabola above is
You can simplify that if your teacher wants you to.
Now you find the equation of the parabola that opens to
the left.
Edwin
