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High school mathematics elective 2- 1 elliptical topic (there must be a detailed process)
1. Let the two focal coordinates of a straight line and an ellipse be A(x 1, y 1).

B(x2,y2)

The midpoint of AB is M(x, y).

The elliptic equation is

X^2

+2y^2=2

Substitute A(x 1, y 1) to get it.

X 1^2

+2y 1^2=2

The same form

Substitute it into B(x2, y2).

X2^2

+2y2^2=2

Second division

One kind-two kinds

(x 1-x2)(x 1+x2)+2(y 1-y2)(y 1+y2)= 0

M(x, y) is the midpoint of AB.

therefore

x=(x 1+x2)/2

y=(y 1-y2)/2

So (x1-x2) 2x+2 (y1-y2) 2y = 0.

The variable k = (y1-y2)/(x1-x2) =-x/y.

Use m

P

Two-point slope

k=(y- 1)/(x-2)

therefore

(y- 1)/(x-2)=-x/y

Simplified to x 2+2y 2-2x-2y = 0.

2. Substitute x=0 into the straight line y=kx+ 1.

Get y= 1

So the straight line passes through the point (0, 1)

As long as (0, 1) is inside or on an ellipse.

Then straight lines and ellipses must have something in common.

therefore

0^2/5

+ 1^2/m

& lt= 1

Solve m>= 1

Or m < 0 (give up

It is not an ellipse at this time)

therefore

m & gt= 1