Question 77889
this is a hyperbola of the form {{{(((y-k)^2)/(a^2))-(((x-h)^2)/(b^2))=1}}}with (h,k) being the center of the graph (mid-way between the vertices)


a is equal to 1/2 the distance between the vertices; and the absolute value of the slope of the asymptote is a/b


so h=4, k=2, a=2, and b=1...the equation is {{{(((y-2)^2)/4)-(((x-4)^2)/1)=1}}}