If the midpoint of line a and B is (1,1), then the equation of L is?

If the midpoint of line a and B is (1,1), then the equation of L is?

Let a (x1, Y1) and B (X2, Y2) be substituted into the elliptic equation, X1 ^ 2 / 9 + Y1 ^ 2 / 4 = 1 (1) x2 ^ 2 / 9 + Y2 ^ 2 / 4 = 1 (2) (1) - (2) be, (x1 + x2) * (x1-x2) / 9 + (Y1 + Y2) (y1-y2) / 4 = 0 (3) be substituted into (3) be k = -

The straight line L: x + 4y-5 = 0 and the ellipse x ^ 2 / 16 + y ^ 2 / 4 = 1 intersect at P and Q, the midpoint m of the line PQ, and calculate the chord length P

x=5-4y
(5-4y)^2/16+y^2/4=1
25-40y+16y^2+4y^2-16=0
20y^2-40y+9=0
PQ = √ [1 + (1 / k)] * √ [(Y1 + Y2) ^ 2-4y1 * Y2] using Vader's theorem
=√（1+1/16）*√（4-9/5）= √935/20

It is known that m [4,2] is the midpoint of the line segment AB cut by the ellipse [x + 4Y = 36], and the equation for solving the line L is obtained
The L equation is
The square of x plus four times the square of Y

This line segment must pass through point M. let y = KX + 2-4k
Let a (x1, Y1) B (X2, Y2) be connected with the elliptic equation
The expression containing K of X1 + x2 can be obtained
Because m is the midpoint of AB (x1 + x2) / 2 = 4
The solution is k = - 1 / 2
So the equation is 2Y + X-8 = 0