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Question 724582: What are the focus and the directrix of the graph of x = 1/24y^2?
focus (0, –6), directrix x = 6
focus (6, 0), directrix x = –6
focus (0, 6), directrix y = –6
focus (–6, 0), directrix y = 6
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! 
Since the y is squared and not the x, the vertex form of the equation is:
(Note: Some books/teachers use "a" or "2p" instead of "4p". But it's not really important if you call it "a", "2p" or "4p" as long as you know what the number represents. The number is 4 times the distance from the vertex to the focus.)
We'll start by rewriting the equation in vertex form. Multiplying by 24 we get:
Since x = x-0 and y = y-0 we can rewrite this as:
Now that the equation is in vertex form we can solve the problem. We can see that the "h" and "k" are 0's so the vertex is (0, 0). We can also see that 4 times the distance from the vertex to the focus is 24. So the distance from the vertex to the focus is 6. As we determined earlier this parabola opens to the right or left. Since the "6" we just found was positive, the focus will be six to the right of the vertex. The point which is six to the right of (0, 0) is (6, 0). Since only one of the provided possible answers has this point as the focus, we know that it is the answer. (If more than one answer had (6, 0) we would then find the directrix. For a parabola that opens to the left or right, the directrix will be a vertical line. And this vertical line will be the same distance from the vertex as the focus is except in opposite direction. The vertical line 6 to the left of (0, 0) is the line x = -6.)
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