Given a = {(x, y) | x2 + y2-6x-8y + 20 = 0}, B = {(x, y) | kx-y-4k + 3 = 0}, then the number of elements of a ∩ B is () A. 0B. 1C. 2D. 3 | Math enthusiast | Mathematical art

Given a = {(x, y) | x2 + y2-6x-8y + 20 = 0}, B = {(x, y) | kx-y-4k + 3 = 0}, then the number of elements of a ∩ B is () A. 0B. 1C. 2D. 3

From x2 + y2-6x-8y + 20 = 0, (x-3) 2 + (y-4) 2 = 5, that is, set a represents the points on the circumference of a circle with (3,4) as the center and 5 as the radius; kx-y-4k + 3 = 0 represents the points on a straight line, and (x-4) K + 3-y = 0 ｜ over the fixed point (4,3), substituting (4,3), (x-3) 2 + (y-4) 2 = 2 < 5

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