Is there a Focal Point/Area/Line of a Parabola for not perpendicular Lines

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I'm not sure if this is mathematical enough for this forum, since it's my first post, but please don't be too harsh!

So my question is: If the incoming lines of a Parabola come in perpendicular to the base, they all get "reflected" to the focal point. Assuming the parabola stays the same shape, but all of the lines come on from a different angle, let's say 70° or 40°, do they meet in a common point, or maybe a line or curve? In more real terms: If I use a parabolic dish to collect sunlight, and rotate it towards the ground - does it still focus the light to specific points and could it potentially burn the ground?

thanks! :)

Ps.: Excuse my English and lack of math-terms, I'm neither native nor very professional at maths.