Let H be a set of hyperbolas, If a relation R on H is defined by R= $\{(h_1,h_2):h_1,h_2$ have same pair of asymptotes, $h_1,h_2\in H\}$, then the relation R is 

R is reflexive as  $h_{1}R{h}_1$ ($h_1, h_2$  have same pair of asymptotes)
R is symmetric c as  $h_{1}R{h}_2\Rightarrow h_{2}R{h}_1$
R is transitive as  $h_{1}R{h}_2$ and  $h_{2}R{h}_3$ 
$\Rightarrow$$h_1, h_2$  have same pair of asymptotes and  $h_2, h_3$ have same pair of asymptotes
$\Rightarrow h_1, h_3$  Have same pair of asymptotes