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

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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Piper Pruitt
The origin of Hyperbola is (0,0) that in centre, with vertex (3,0)
The standard equation for a hyperbola is
$\frac{{x}^{2}}{{a}^{2}}-\frac{{y}^{2}}{{b}^{2}}=1$
Now, as the vertex is (3,0) which gives:
a=3
Further, Asymptotes are given as

Hence slope of the Asymptotes =b/a
equation of Hyperbola is
$\frac{{x}^{2}}{9}-\frac{{y}^{2}}{16}=1$