Given that the straight line X-my + 3 = 0 and the circle x ^ + y ^ - 6x + 5 = 0.1, when the straight line is tangent to the circle, find the value of the real number M | Math enthusiast | Mathematical art

Given that the straight line X-my + 3 = 0 and the circle x ^ + y ^ - 6x + 5 = 0.1, when the straight line is tangent to the circle, find the value of the real number M

Circle x ^ + y ^ - 6x + 5 = 0 (x-3) ^ 2 + y ^ 2 = 4
The radius of center coordinate (3,0) r = 2
When the line is tangent to the circle, the distance from the center of the circle to the line d = R
d=|6|/√(1+m^2)=2
3=√(1+m^2)
9=1+m^2
m^2=8
m=±2√2

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