Q Find the equation of the hyperbola with centre as the origin, transverse axis along x - axis, ecentricity √5 and the sum of whose semi - axes is 9.

the centre of the hyperbola is (0,0).
and the transverse axis is along x-axis, i.e. y =0
therefore let the equation of the hyperbola be $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1..............\left(1\right)$
given : $e=\sqrt{5} and a+b=9$
$$\begin{gathered} b^2=a^2(e^2-1) \\ \frac{b^2}{a^2}=5-1=4 \\ \frac{b}{a}=2 \\ b=2a \\ a+2a=9 \\ 3a=9\Rightarrow a=9/3=3 \end{gathered}$$
b= 2*3=6
thus the required equation of the hyperbola is 
$$\begin{gathered} \frac{x^2}{3^2}-\frac{y^2}{6^2}=1 \\ \frac{x^2}{9}-\frac{y^2}{36}=1 \end{gathered}$$
which is the required equation of the hyperbola.

hope this helps you.