You're confusing the equilibrium constant and the rate constant. Only a change in temperature can affect the equilibrium constant (K...capital K). It won't be affected by a change in activation energy. If you add a catalyst it lowers the activation energy in both directions but doesn't shift the overall equilibrium in either direction. You will still have the same ratio of products to reactants when you reach equilibrium; you will just reach equilibrium more quickly.
The Arrhenius equation involves the rate constant (k...lowercase k) rather than the equilibrium constant and shows that rate constants can be affected by a change in either temperature or activation energy.
Hope this helps!
