What are the focus and directrix of the parabola with the given equation?
x equals negative 1 over 8 y squared
A. focus (0, 2): directrix: x = –2
B. focus (0, 2): directrix: x = 0
C. focus (2, 0): directrix: x = 2
D. focus (–2, 0): directrix: x = 2
To determine the focus and directrix of the parabola with the given equation x = -1/8y^2, we first rewrite the equation in standard form.
The standard form of a parabolic equation with the vertex at the origin (0,0) is x = 4p*y^2, where (0,p) is the focus.
In this case, x = -1/8y^2 can be rewritten as x = -1/8(1/4)y^2, so we have p = -1/4 and the focus is at (0, -1/4).
Therefore, the correct answer is:
A. focus (0, -1/4): directrix: x = –2