Zenmo
  • Zenmo
Find the standard form of hyperbola equation with the center at origin. Given characteristics are, foci: (0, -8) , (0, 8); asymptotes y=4x, y=-4x .
Mathematics
chestercat
  • chestercat
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Loser66
  • Loser66
What is the standard form of a hyperbola?
Zenmo
  • Zenmo
|dw:1433417287155:dw|
Loser66
  • Loser66
in this case, k = h =0 ok?

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Zenmo
  • Zenmo
For asymptotes: |dw:1433417392634:dw|
Loser66
  • Loser66
and \(c^2 = a^2+b^2\) right?
Loser66
  • Loser66
you have \(a^2 + b^2 = 64\\\dfrac{a}{b}=4\) can you find a, b?
Loser66
  • Loser66
Please, no assuming, solve it algebraically,
Zenmo
  • Zenmo
|dw:1433417547097:dw|
Zenmo
  • Zenmo
|dw:1433417613972:dw|
Loser66
  • Loser66
yup
Zenmo
  • Zenmo
|dw:1433417709955:dw|
Loser66
  • Loser66
we need b^2 to plug in the formula, no need to find b
Loser66
  • Loser66
nope
Loser66
  • Loser66
\(b^2 = 64/17\) \(c^2 = a^2 +b^2\\a^2 = c^2 - b^2 = 64 -64/17 = 1024/17\)
Zenmo
  • Zenmo
|dw:1433418156536:dw| So |dw:1433418261218:dw| then final equation is |dw:1433418336166:dw|
Zenmo
  • Zenmo
Thanks! :D

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