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mixas84 [53]
3 years ago
14

What is the equation of the quadratic graph with a focus of (5, −1) and a directrix of y = 1?

Mathematics
2 answers:
pav-90 [236]3 years ago
5 0
(x-h)^2=4p(y-k)
vertex is (h,k)
p is the distance from focus to vertex and distance from vertex to directix (vertex is in middle of directix and focus)
if p is positive, the parabola opens up and the focus is above the directix
if p is negative, the parabola opens down and the focus is below the directix
 
we see the directix is over the focus (1>-1) so the parabola opens down and p is negative
distance from (5,-1) to y=1 is 2 units
2/2=1
p=-1 since p is negative
1 up from (5,-1) is (5,0)
veretx is (5,0)
(x-5)^2=4(-1)(y-0)
(x-5)^2=-4y is the equation
Lemur [1.5K]3 years ago
4 0
The answer is <span>directrix is horizontal, so the parabola is vertical </span>
<span>focus lies below the directrix, so the parabola opens downwards. </span>

<span>General equation for down-opening parabola: </span>
<span> y = a(x-h)²+k </span>
<span>with </span>
<span> a<0 </span>
<span> vertex (h,k) </span>
<span> focal length p = 1/|4a| </span>
<span> focus (h,k-p) </span>
<span> directrix (h,k+p) </span>

<span>Apply your data and solve for h, k, and a. </span>
<span>vertex is halfway between focus and directrix: (3,3) </span>
<span>h = 3 </span>
<span>k = 3 </span>

<span>distance between focus and vertex is 2, so p = 2. </span>
<span>a = -1/(4p) = -⅛ </span>

<span>y = -⅛(x-3)²+3 </span>
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