SOLUTION: Find the vertex, focus, and directrix of th eparabola given by the equation x^2 - 8x -16y + 0

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Question 857853: Find the vertex, focus, and directrix of th eparabola given by the equation
x^2 - 8x -16y + 0
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Something is missing. An red%28equa%29tion must have an red%28equa%29l sign.
Maybe you meant to type x%5E2+-+8x+-16y=+0 and you got a + sign instead of the = sign.

x%5E2-8x-16y=0<-->x%5E2-8x=16y<-->x%5E2-8x%2B16=16y%2B16<-->%28x-4%29%5E2=16%28y%2B1%29<-->y%2B1=%281%2F16%29%28x-4%29%5E2<-->y=%281%2F16%29%28x-4%29%5E2%7D-1
is the equation of a parabola with the vertical axis of symmetry
x-4=0<-->x=4 ,
the vertex at (4,-1), which is the lowest value y can take,
and a focal distance of 16%2F4=4 .
That means that the focus is (4,3),
4 units above the vertex,
and the directrix is the line y=-5 ,
4 units below the vertex.