Question 113439
the center of the hyperbola (h,k) is the intersection of the asymptotes, (1,2)


the parabola passes through (4,2) which is directly above the center
___ this means an East-West opening parabola of the form {{{(((x-h)^2)/a^2)-(((y-k)^2)/b^2)=1}}}
___ the slope of the asymptotes is ±(b/a), so b=2a and b^2=4a^2


(((4-1)^2)/(a^2))-(((2-2)^2)/(4a^2))=1 ___ ((3^2)/(a^2))-0=1 ___ 3^2=a^2 ___ 3=a ___ so b=6


{{{(((x-1)^2)/9)-(((y-2)^2)/36)=1}}}