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Senior high school mathematics conic topic
Let the coordinates of a and b be (xA, yA), (xB, yB).

Then xa 2-ya 2/2 = 1.

xB^2 - yB^2/2 = 1

Up-down type

xA^2 - xB^2 = (yA^2 - yB^2)/2

(yA - yB)/(xA - xB) = 2(xA + xB)/(yA + yB)

M( 1, 2) is the midpoint of line segment AB.

And xA+xB = 2.

yA+yB = 4

(yA - yB)/(xA - xB) = 1

∴AB slope = 1

The midpoint of AB is (1, 2).

∴AB:y = x + 1

The equation is x-y+ 1=0.

CD is the middle vertical line of line segment AB.

∴CD slope is-1.

The CD equation is x+y-3=0.

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