The equation of hyperbola is
[tex]\frac{(x-h)^2}{a^2}- \frac{(y-k)^2}{b^2}=1[/tex]
Where center is (h,k)
Vertex is(h+a,k)
SO if we compare the vertex with the vertex formula, we will get
[tex]h+a=9, k=0[/tex]
And formula of focus is (h+c,k)
On comparing we will get
[tex]h+c=41[/tex]
So we have h =0 , k=0, a=9, c=41
[tex]b^2=c^2-a^2\\b^2=41^2-9^2\\b^2=1600[/tex]
So the equation is
[tex]\frac{x^2}{81}-\frac{y^2}{1600}=1[/tex]
