Is the focal length of hyperbola 2C or C

Is the focal length of hyperbola 2C or C

The focal length is 2C
C is called half focus
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P is a point on the left branch of the hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1. F1 and F2 are the left and right focus respectively. The focal length is 2C
P is a point on the left branch of hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1, F1 and F2 are the left and right focus respectively, and the focal length is 2C

Let the center coordinates of the inscribed circle O '(x, y)
Easy to know F1 (- C, 0), F2 (C, 0)
Make the vertical lines of Pf1, PF2 and F1F2 through o 'and intersect e, F, g respectively,
Then, 2A = pf2-pf1 = f2g-f1g = (C-X) - (c + x) = - 2x, that is, x = - A
The abscissa of the center is - A

It is known that hyperbola C: x ^ 2 / 2-y ^ 2 / 2 = 1, mark 0 as the coordinate origin, and the line L passing through Q (0,2) intersects hyperbola C at two different points E and F
If the area of △ OEF is 2 √ 2, find the equation of line L

Let the linear equation be Y-2 = K (x-0), that is, y = KX + 2 be substituted into the hyperbolic equation, and the simplification is as follows: (1-k ^ 2) x ^ 2-4kx-6 = 0 | EF | = √ 1 + K ^ 2 * √ (4K / 1-k ^ 2) ^ 2-4 * (- 6 / 1-k ^ 2) let K ^ 2 = m | EF | = √ (- 8m ^ 2 + 16m + 24) / (1-m)