If the line L and the ellipse x ^ 2 / 4 + y ^ 2 = 1 intersect at two points P and Q and l passes through the fixed point (1,0), then the trajectory equation of the middle point of the chord PQ is only solved by the great God

Let the coordinates of the midpoint of the chord PQ (x, y), P (x1, Y1), q (X2, Y2)
Let L: y = K (x-1)
Simultaneous y = K (x-1) and X & sup2 / 4 + Y & sup2; = 1
By eliminating y, we get: (1 + 4K & sup2;) x & sup2; - 8K & sup2; X + 4K & sup2; - 4 = 0
From the question △ > 0
Weida theorem: X1 + x2 = 8K & sup2; / (1 + 4K & sup2;)
x1x2=(4k²-4)/(1+4k²)
x=(x1+x2)/2=4k²/(1+4k²)
y=(y1+y2)/2=[k(x1-1)+k(x2-1)]/2=[k(x1+x2)-2k]/2=-k/(1+4k²)
x/y=4k²/-k
k=-x/4y
k²=x²/16y²
Because x = 4K & sup2; / (1 + 4K & sup2;) eliminates K & sup2; and reduces it to 4Y & sup2; + X & sup2; - x = 0

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