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How do I solve this question on hyperbolas?
I need to create and equation in standard form which satisfies the given information. But I am completely lost. what I know is Center= (1, -4), c=6, and e=2, as well as that it has a horizontal focal axis.
1 Answer
- DWReadLv 78 years agoFavorite Answer
You need to know the orientation of the hyperbola.
The foci are horizontally aligned, so the hyperbola is horizontal.
General equation of a HORIZONTAL hyperbola:
(x - h)²/a² - (y - k)²/b² = 1
with
center (h, k)
c² = a² + b²
e = c/a
Match your data to the equation.
center (h, k) = (1, -4)
h = 1
k = -4
e = c/a
2 = 6/a
a = 3
c² = a² + b²
6² = 3² + b²
b² = 27
The equation becomes
y²/9 - x²/27 = 1
