Question 885230: Find the center, foci, vertices, and asymptotes of the hyperbola.
x^2 - y^2 = 8(x-y) + 1
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website! x^2 - y^2 = 8(x-y) + 1
(x+4)^2 - (y + 4)^2 = 1 + 16 -16
(x+4)^2 - (y + 4)^2 = 1
Standard Form of an Equation of an Hyperbola opening right and left is:
 with C(h,k) and vertices 'a' units right and left of center, 2a the length of the transverse axis. e = c/a.
Foci are  = c- units right and left of center along y = k
& Asymptotes Lines passing thru C(h,k), with slopes m = ± b/a
C(4,4) a = 1, b = 1
V(3,4) and (5,4)
foci(4+√2, 4) and (4-√2, 4)
asymptotes: m = ± b/a = ± 1
y - 4 = (x-4), y = x
y - 4 = -(x-4), y = x + 8
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