SOLUTION: what is the vertex directrix and focus of the equation (x+5)^2=4y

Question 1012164: what is the vertex directrix and focus of the equation (x+5)^2=4y
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

....compare to and you see that and
so, vertex is at (,
or, we can use standard form and calculate coordinates of the vertex like this:

the x-coordinate of the focus is:

then, y-coordinate is

so, we got same result for vertex

the focus is:
The focus lies on the axis of symmetry of the parabola, and has the y-coordinate . Because we just found the vertex to be (,), we know the axis of symmetry to be , and the focus lies on that line.
y-coordinate is at
and the coordinates of the focus are:(,)

Once you know the y=coordinate of the vertex, , it is given by , where . Thus, as we calculated for the focus, above:

and the directrix is

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