According to the standard equation of hyperbola and the left focus -2 0

Find the value of a

Because a 2+b 2 = c 2.

So a 2+ 1 = 4.

A>0 So a=√3

The equation of hyperbola is x 2/3-y 2 = 1

Set point Px y][x≥√3]

Then x 2/3-y 2 =1.

y^2=x^2/3- 1

fp=x[x+2]+y^2 opx

=4/3x^2+2x- 1

=4/3[x+3/4]^2-7/4

And because x≥√3.

X=√3 has a minimum value.

3+2√3

So the value range is 3+2√3, +∞)