If the line X-my + 3 = 0 and the circle (x-3) ^ 2 + y ^ 2 = 4 are separated, then the value range of real number m is

If the line X-my + 3 = 0 and the circle (x-3) ^ 2 + y ^ 2 = 4 are separated, then the value range of real number m is

6/(m^2+1)^(1/2)>2
m^2

Given that the line X-2 √ 2Y + 3M = 0 intersects the circle x ^ 2 + y ^ 2-6x + 5 = 0, the value range of M is

Substituting x = 2 √ 2y-3m into a circle
(2√2y-3m)^2+y^2-6(2√2y-3m)+5=0
9y^2-(12m√2-12√2)y+9m^2+18m+5=0
Δ=144*2(m^2-2m+1)-4*9(9m^2+18m+5)
From Δ > = 0
-m^2-34m+3>=0
-17-2√73

Let's discuss the relationship between the line X-my + 2 = 0 and the circle x ^ 2 + y ^ 2 = 4 on the value of M. thank you,

When m = 0, the tangent point is (- 2,0); when m is not 0, it intersects

Let m > 0, then the position relation between the line 2 (x + y) + 1 + M = 0 and the circle x2 + y2 = m is ()
A. Tangency B. intersection C. tangency or separation D. intersection or tangency

The distance between the center of the circle and the straight line is d = 1 + m2, the radius of the circle is m. ∵ D-R = 1 + m2-m = 12 (m-2m + 1) = 12 (m-1) 2 ≥ 0, and the position relationship between the straight line and the circle is tangent or separated