The line y-x-2=0 cuts the circle x² + y2 - 8x + 4y - 14 = 0 at points A and B with B is in the first quadrant.
a) Find the point of intersection of the tangent of the circle that passes through A
and B.​

Iwould like to think so. what’s the question you need with?

Idon't see any graph, however the graph of the function : f(x) = x²-2x+3 is a parabola: 1) open upward (since a> 0)2) it intersects y-axis in 3 (y=3)3) its axis of symmetry is x = +1 ( -b/2a)4) it's minimum is y = -2, so its vertex is (1,-2)5) it doesn't intersect the x-axis since discriminant < 0