When the line X-my + 3 = 0 and the circle x ^ 2 + y ^ 2-6x + 5 = 0 intersect, tangent and depart from the circle respectively, the range of M is calculated The process

When the line X-my + 3 = 0 and the circle x ^ 2 + y ^ 2-6x + 5 = 0 intersect, tangent and depart from the circle respectively, the range of M is calculated The process

x^2+y^2-6x+5=0
->(x-3) ^ 2 + y ^ 2 = 4 is a circle with radius 2 and center (3,0)
Therefore, we only need to find out the distance from the center of the circle to the straight line, and divide it into three categories: greater than 2, equal to 2, less than 2, and solve m respectively, that is, the range of M of separation, tangency, and intersection
The distance expression is 6 / (1 + m ^ 2) ^ (1 / 2), then the solution is
The final answer should be intersection: m is greater than double root sign 2 or less than negative double root sign 2; tangency is m equal to positive and negative double root sign 2; separation is m greater than negative double root sign 2 and less than positive double root sign 2