Question 757924
find the formula for a hyperbola with foci on the y axis given that the asymptotes are y=+-5/3x 
what are the coordinates of the foci (hint leave these radicals they wont be integers)
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Given hyperbola has a vertical transverse axis.
Its standard form of equation: {{{(y-k)^2/a^2-(x-h)^2/b^2=1}}}, (h,k)=(x,y) coordinates of center.
Given slope of asymptotes={{{5x/3=a/b}}}
{{{b=3a/5x}}}
{{{c^2=a^2+b^2=(a^2+(9a^2)/(25x^2))=(25x^2a^2+9a^2)/(25x^2)=a^2(25x^2+9)/(25x^2)}}}
{{{c=a*sqrt(25x^2+9)/(5x)}}}
coordinates of foci: (h, kąc) (coordinates of center not given)