It is known that the center of hyperbola is at the origin, the eccentricity is 2, and a focus f (- m, 0) Given that the center of the hyperbola is at the origin, the eccentricity is 2, a focus f (- m.0) (M is a normal number) 1 helps to solve the hyperbolic equation 2. Let Q be a point on the hyperbola, and the line L passing through the points F and Q intersects the Y axis at the point M. if MQ = 2qf, help to solve the L equation

It is known that the center of hyperbola is at the origin, the eccentricity is 2, and a focus f (- m, 0) Given that the center of the hyperbola is at the origin, the eccentricity is 2, a focus f (- m.0) (M is a normal number) 1 helps to solve the hyperbolic equation 2. Let Q be a point on the hyperbola, and the line L passing through the points F and Q intersects the Y axis at the point M. if MQ = 2qf, help to solve the L equation

one
F (- m, 0) m > 0, centered at O (0,0)
c=m
e=2=c/a
a=c/e=m/2
x^2/(m^2/4)-y^2/(m^2-m^2/4)=1
4x^2/m^2-4y^2/3m^2=1
two
Through f line: y = K (x + m)
x=0,y=km,M(0,km)
MQ=2QF
Qx=(Fx+2Mx)/(1+2)=-m/3
Qy=(Fy+2My)/(1+2)=2km/3
4*(2km/3)^2/m^2- 4*(-m/3)^2/3m^2=1
16k^2/9-4/9=1
16k^2=13/9
k^2=13/144
K = √ 13 / 12 or K = - √ 13 / 12
50: Y = (√ 13 / 12) (x + m) or y = (- √ 13 / 12) (x + m)