Given the elliptic equation x ^ 2 / 2 + y ^ 2 / 3 = 1, try to determine the value range of B, so that there are two different points on the ellipse, a and B are symmetric about the straight line y = 4x + B

Use the point difference method!
Let a (x1, Y1) B (X2, Y2), AB midpoint m (x0, Y0)
(x1)^2/2+(y1)^2/3=1...1
(x2)^2/2+(y2)^2/3=1...2
1-2 is (1 / 2) (x1 + x2) (x1-x2) + (1 / 3) (Y1 + Y2) (y1-y2) = 0
KAB = (x1-x2) / (y1-y2) = (1 / 2x0) / (- 1 / 3y0) = - 1 / 4 (middle vertical)
Launch Y0 = 6x0 launch m (x0,6x0)
M is on L again
Substituting into L equation m (- B, - 6B)
Finally, M is substituted into the elliptic equation to make it less than 1
The range of B
I bet it's right, our teacher said it!

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