To find the equation of a parabola with focus (0,4) and directrix y=2, we first need to determine the distance between the focus and the directrix, which is the same as the distance between the vertex and the directrix.
The vertex of the parabola will be halfway between the focus and the directrix, so the vertex will be at (0,3).
Since the directrix is a horizontal line and the focus is 2 units above the directrix, the parabola will open upwards.
The equation of a parabola with vertex (h,k), focus (h, k+p), and directrix y=k-p is (x-h)^2 = 4p(y-k).
In this case, h=0, k=3, p=1 (since the focus is 1 unit above the vertex), so the equation will be of the form x^2 = 4(y-3).
Expanding this equation gives the standard form equation of the parabola:
x^2 = 4y - 12
Therefore, the equation in standard form that matches the parabola with focus at (0,4) and the directrix y=2 is:
y = 1/4x^2 + 3.
Rico is drafting a parabola on a coordinate plane. He wants the focus to be at (0,4)
and the directrix to be y=2
. What will be the equation, in standard form, that matches this parabola? Fill in the missing values of the equation.(1 point)
y=
x2+3
1 answer
1 answer