Since the patio is on the north side(I am taking for granted you live in the Northern Hemisphere), any sunlight will be indirect. That means it reflects from whatever is north of the house.
If the covering were on the south(meaning too close/high would shade the house from direct sun), the answer would be to use a pole as long as the new patio cover is high and find the spot away from the house so the top of the shadow caused by the pole does not show on the house.
That would not be possible on the other side(shadow from the pole would show away from the house).
I'd say(if the covering is not attached to the house), the distance should be at least halfway out of the shadow of the roof on your house.
Q
