SOLUTION: What is the equation of the directrix of the parabola given by the equation (y - 3)^2 = 8(x - 5)?

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Question 936457: What is the equation of the directrix of the parabola given by the equation (y - 3)^2 = 8(x - 5)?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
First we have to graph the parabola:

[Always draw graphs when doing conic section problems].

%28y+-+3%29%5E2+=+8%28x+-+5%29

Compare it to 

%28y+-+k%29%5E2+=+4a%28x+-+h%29

So the vertex is (h,k) = (5,3).

It opens to the right because 4a=8 or a=2 is positive.

So we sketch in the parabola with vertex (5,3).



|a|=2 is the distance from both the vertex to both the focus and the directrix.
The focus is a point inside the parabola and the directrix is a line
outside the parabola line, which are the green point and line drawn below:



So as we see from the graph, the focus is (7,3) and the directrix is x=3.

I went ahead and found the focus because in other problems you will have
to find the focus.

Edwin