Given that the straight line with slope 2 intersects with hyperbola x ^ 2-y ^ 2 = 12 at P1 and P2, find the trajectory equation of the midpoint of line p1p2

Given that the straight line with slope 2 intersects with hyperbola x ^ 2-y ^ 2 = 12 at P1 and P2, find the trajectory equation of the midpoint of line p1p2

Let the linear equation be y = 2x + B
Take straight line into hyperbola X & # 178; - Y & # 178; = 12
We get: 3x & # 178; + 4bx + B & # 178; + 12 = 0
Because there is a solution, the discriminant is ＞ 0, that is, 16b & # 178; ＞ 12 (B & # 178; + 12), B ＞ 6 or ＜ - 6
The abscissa x = (x1 + x2) / 2 = - 2b / 3, x > 4 or x < - 4 of the midpoint of p1p2
The ordinate of the midpoint of p1p2 is y = - B / 3