Find the equation of a hyperbola satisfying the given conditions. Asymptotes y=4/3x, y=-4/3x, one vertex (3,0)

gebuiteldmz 2022-10-02 Answered
Find the equation of a hyperbola satisfying the given conditions.
Asymptotes y=4/3x, y=-4/3x, one vertex (3,0)
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Answers (1)

Piper Pruitt
Answered 2022-10-03 Author has 9 answers
The origin of Hyperbola is (0,0) that in centre, with vertex (3,0)
The standard equation for a hyperbola is
x 2 a 2 y 2 b 2 = 1
Now, as the vertex is (3,0) which gives:
a=3
Further, Asymptotes are given as
y = + 4 3 x  and  y = 4 3 x or  y = ± 4 3 x
Hence slope of the Asymptotes =b/a
equation of Hyperbola is
x 2 9 y 2 16 = 1
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