Given the hyperbola x ^ 2-y ^ 2 = 1, the slope of the straight line L is 1 / 2, and it intersects with the hyperbola at a and B, find the equation satisfied by the midpoint of ab I want to use the point difference method, but how can I use hyperbola? If it's an ellipse, I'll do it

Let the line be y = x / 2 + M
The joint equation y = x / 2 + m and x ^ 2-y ^ 2 = 1 eliminate X and obtain a quadratic cubic equation of one variable with respect to y
Let a (x1, Y1) B (X2, Y2)
Because a and B are the intersection of straight line and hyperbola
Then the midpoint is ((x1 + x2) / 2, (x1 + x2) / 4 + m / 2)
So X1 and X2 are the two parts of the equation three. We use m to express X1 + x2 and substitute it into the middle point to simplify the equation of the middle point

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