Classical Elliptic Problems in Senior High School Mathematics (Difficult)

Let the midpoint of B(X 1, Y 1)D(X2, Y2)BD be N(x0, y0).

∫B, d in ellipse x? /4+3y？ /4= 1

∴{x 1？ /4+3y 1？ /4= 1①

x2？ /4+3y2？ /4= 1②

①-② Acquisition

(x 1-x2)(x 1+x2)/4=﹣3(y 1-y2)(y 1+y2)/4

(x 1-x2)(x 1+x2)=﹣3(y 1-y2)(y 1+y2)

﹣ 1/3 =(y 1-y2)(y 1+y2)/(x 1-x2)(x 1+x2)

That is kbd * kon =- 1/3.

Question KAC = Tan 135 =- 1

Let AC: y =-x+b

Ac intersection (1, 2)

∴AC:y=﹣x+3

Ac vertical BD

∴KBD= 1, which means kon = ∴ 1/3.

Because n is on ac

That is x0+y0-3 = 0.

yo/x0=﹣ 1/3

∴x0=9/2y0=﹣3/2

BD:y=x﹣6