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vlada-n [284]
3 years ago
7

The equation of a parabola is given.y=1/8x^2+4x+20 What are the coordinates of the focus of the parabola?

Mathematics
2 answers:
Lena [83]3 years ago
8 0
He equation of a parabola is x = -4(y-1)^2. What is the equation of the directrix? 
<span>You may write the equation as </span>
<span>(y-1)^2 = (1) (x+4) </span>
<span>(y-k)^2 = 4p(x-h), where (h,k) is the vertex </span>
<span>4p=1 </span>
<span>p=1/4 </span>
<span>k=1 </span>
<span>h=-4 </span>

<span>The directrix is a vertical line x= h-p </span>
<span>x = -4-1/4 </span>
<span>x=-17/4 </span>

<span>------------------------------- </span>
<span>What is the focal length of the parabola with equation y - 4 = 1/8x^2 </span>
<span>(x-0)^2 = 8(y-4) </span>
<span>The vertex is (0,4) </span>
<span>4p=8 </span>
<span>p=2 (focal length) -- distance between vertex and the focus </span>
<span>------------------------------- </span>
<span>(y-0)^2 = (4/3) (x-7) </span>
<span>vertex = (7,0) </span>
<span>4p=4/3 </span>
<span>p=1/3 </span>
<span>focus : (h+p,k) </span>
<span>(7+1/3, 0)</span>
Romashka-Z-Leto [24]3 years ago
4 0
Convert it to  vertex form we get 

y = 1/8(x + 16)^2 - 12     

so the vertex is at (-16,-12) and  the x coordinate of the focus will be -16)

The focus  will be at (-16, k + p)    Here k = -12 from the vertex equation and  p  = 1 / 4a  where a = 1/8    so p = 1 / 1/2 = 2  So k + p = -12 + 2 = -10

So the coordinates of the focus are (-16, -10) answer


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