jade57 jade57
  • 17-08-2017
  • Mathematics
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The vertex and the focus and the directix

The vertex and the focus and the directix class=

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apologiabiology
apologiabiology apologiabiology
  • 17-08-2017
get into form (x-h)²=4p(y-k)
(h,k) is vertex

p is disatnace from focus to vertex and vertex to directix

if p is negative, then directeix is above focus
if p is positive the directix is below focus

so
x²+20y=10
x²=-20y+10
(x-0)²=4(-5)(y-0.5)
vertex is (0,0.5)
-5<0 so directix is above focus and above the vertex
it is 5 units above the vertex
so it is at y=5.5
the focus is 5 units below the vertex
it is at (0,-4.5)



vertex is (0,0.5)
focus is (0,-4.5)
directix is y=5.5
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