The midpoint chord problem generally uses the point difference method to find the slope of the straight line.

Taking an ellipse as an example, the elliptic equation x 2/a 2+y 2/b 2 =1,(A > b>0).

Let the straight line L intersect the ellipse at a(x 1, y 1), b(x2, y2), and the midpoint n(x0, y0).

x 1^2/a^2+y 1^2/b^2= 1

x2^2/a^2+y2^2/b^2= 1

Subtract two expressions

(x 1+x2)(x2-x 1)/a^2+(y2+y 1)(y2-y 1)/b^2=0

x 1+x 1=2x0，y 1+y2=2y0

kab=(y2-y 1)/(x2-x 1)=-b^2*

x0/(a^2*

y0)

Ab equation

y-y0=-b^2*

x0/(a^2*

y0)(x-x0)

The slope of the midpoint chord of a hyperbola can be obtained by analogy.

b^2*

x0/(a^2*

y0)

Parabolic midpoint chord slope

p/y0