Question

how do i determine the point of intersection of a circle with a radius of 14 and the line coming in at a 35 degree angle

Answer 1

depends on the line. You have the slope of the line, but no idea where it is. Maybe it doesn't even intersect the circle.

Answer 2

Now, if the line goes through the center of the circle, and the center of the circle is at (0,0) then they intersect at

(14cos35°,14sin35°)

Naturally, if the center is at (h,k) then they intersect at

(h+14cos35°,k+14sin35°)

Also, they intersect at a point diagonally opposite from the above. If the line does not go through the center, then all bets are off.