Post a New Question

precalc

posted by .

what is the directrix and focus of the equation 1/16(y+4)^2=x-3

  • precalc -

    Perform a substitution
    x' = x-3
    y' = y+4
    and you are left with the equatiom
    y'^2 = 16x'

    This is the equation of a parabola with axis along the line y = -4 and vertex at (x',y') = (0,0)
    which is (x,y) = (3,-4)

    The factor 16 tells you where the focus and directrix are.
    16 = 4p,
    where p is the distance from the vertex to the focus and directrix.

    That puts the focus at (x,y) = (7,-4)
    The directrix is the vertical line x = -1

Answer This Question

First Name
School Subject
Your Answer

Related Questions

More Related Questions

Post a New Question