Find the focus and directrix of the parabola

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The parabola given by the equation (y+2)² = 16(x-1) has a vertex at (1, -2) and a focus at (5, -2). The value of 'a' is calculated as 4, leading to the directrix being the line x = -3. The focus and directrix have been correctly identified based on the standard form of a parabola. The discussion confirms that the problem has been solved accurately. The final answer includes both the focus and the directrix.
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Homework Statement



find the focus and directrix of the parabola:
(y+2)^2 = 16(x-1)

Homework Equations



(y-k)^2= 4a(x-h)
focus: ( h+a,k)
vertex: (h,k)

The Attempt at a Solution


k=-2,h=1,a=16/4=4!,
vertex at (1,-2)
focus ( 5,-2)
does that mean that i solved the problem or do i still to do more work to reach the final answer? thanks in advance.
 
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Well, did you find the focus and directrix?
 
i think i did , don't you think so ?
 
The directrix is a line. You don't have any line equations in your answer.
 
directrix : x=h-a
= 1-4
= -3 ? how about this, does look right to you, or am i wrong ?
 
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