Posted by **95** on Friday, December 16, 2011 at 10:50pm.

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

- precalc -
**drwls**, Saturday, December 17, 2011 at 12:07am
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

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