How do you write an equation for a hyperbola that involves foci?

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How do you write an equation for a hyperbola that involves foci?

Mathematics
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@jim_thompson5910 plz help you're the best
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Other answers:

Foci |dw:1435360096843:dw|
vertices |dw:1435360133480:dw|
what is the midpoint of the vertices? |dw:1435360163097:dw|
(4,0) ???
4 is correct 0 is not
(4,5)
good
|dw:1435360285728:dw|
The distance from the center to either vertex is what numeric value?
Ok I understand that the top half of the equation with be (x-4)^2 - (y-5)^2
correct
The distance from either vertex is two?
from center to vertex (pick one) is 2 units, yes
so a = 2 where \[\Large \frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1\]
'a' corresponds to the x portion because the hyperbola opens along the x axis direction (ie horizontally)
c = 3 because it is 3 units from the center to either focus use a^2 + b^2 = c^2 to find b
actually you don't need to solve for b you can stop at b^2 and that would be fine too
@jim_thompson5910 oh okay! i clearly understand now!! thank you :)
no problem

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