What is the distance from an airport from which an airliner climbs above 550 m?
For the landing is quite easy.

Airliners usually approach an airport descending along $3^\circ$ slopes. This means that they will be 300m AGL approximately 5.7km before the runway threshold, and they will be at 550m AGL about 10.5km before the same point.

For the take-off the situation is a bit more complicated, as each aircraft will have a different performance. Taking a value of about 1000ft/min for the vertical velocity and 200Kts for the forward velocity (in aviation we use the imperial system, for a bit of background see here) we get similar distances to the above (it is a $2.8^\circ$ slope)

Note that these paths are more or less a straight continuation of the runway, particularly on the landing side (less so on the take off side).

Each airport has approach and departure procedures, you could try to have a look at those. They are usually published by Jeppesen.