Question 752064
Find the equation of a hyperbola with center
(4, 3), vertex (4, 7) and asymptote y-3=4/5(x-4).
hyperbola has a vertical transverse axis.
Its standard form of equation: {{{(y-k)^2/a^2-(x-h)^2/b^2=1}}}
a=4 (distance from center to vertex on vertical transverse axis)
a^2=16
slope of asymptote=4/5=a/b
b=5a/4=5
b^2=25
For given hyperbola:
Equation: {{{(y-3)^2/16-(x-4)^2/25=1}}}