It is known that m (4,2) is the midpoint of line AB cut by ellipse x2 + 4y2 = 36, then the equation of line L is______ ．

Let K be the slope, then the equation of the line L is Y-2 = K (x-4), that is kx-y + 2-4k = 0, and the equation of the ellipse is reduced to & nbsp; (1 + 4k2) x2 + (16k-32k2) x + 64k2-64k-20 = 0, and the solution is k = - 12, so the equation of the line L is & nbsp; X + 2y-8 = 0, so the answer is x + 2y-8 = 0

It is known that the line L passing through the point m (2,1) and the ellipse x ^ 2 + 4Y ^ 2 = 36 intersect at points a and B, and the line AB just takes m as the midpoint. The equation of the line L is

Let a (x1, Y1), B (X2, Y2), then X1 & # 178; + 4Y1 & # 178; = 36 x2 & # 178; + 4y2 & # 178; = 36 subtract the two formulas to get: (x1 + x2) (x1-x2) + 4 (Y1 + Y2) (y1-y2) = 0 ∵ X1 + x2 = 4 Y1 + y2 = 2 ∵ 4 (x1-x2) ∵ slope k = (y1-y2) / (x1-x2) = - 1 / 2, so the linear equation is: Y -

Given that the point (4, 2) is the midpoint of the line segment cut by the ellipse x236 + Y29 = 1, then the equation of the line L is ()
A. x-2y=0B. x+2y-4=0C. 2x+3y+4=0D. x+2y-8=0

There are two points a (x1, Y1), B (X2, Y2), a (x1, Y1), B (X2, Y22) where a line L and ellipse intersect at two points a (x1, Y1, Y1), a (x1, Y1, Y1), B (X2, Y1), B (X2, Y1), B (X2, Y22), B (X2, Y22), B (X2, Y22). To the elliptic equation, you can get x2136 + y2136 + y219 = 1, x2236 + x2236 + y2236 + y2236 + y229 = 1 = 1, x2236 + y2236 + y229 = 1, two formula subtraction (x1 + x2) (x1 + x2) (x1 + x2) (x1 + x2) (x1 + x2) (x1 + x2) (x1 + x2136 + y2136 = 1 = 1 = 1, x2136 = 1, x2136 = 1, x2136 = 1, x2236 = 1, x2236 = 1, x2236 + x2236 + x2236 + x2236 + x2d

Given that m (4,2) is the midpoint of the line segment cut by the square of ellipse x + 4 times the square of y = 36, the equation of line L is obtained
Urgent, please answer as soon as possible

y-2=k(x-4)
y=kx+2-4k
So (1 + 4K & sup2;) x & sup2; + 8K (2-4k) x + 4 (2-4k) & sup2; - 36 = 0
Midpoint abscissa = (x1 + x2) / 2 = - 4K (2-4k) / (1 + 4K & sup2;) = 4
2k-4k²=-1-4k²
k=-1/2
So x + 2y-8 = 0

It is known that m (4,2) is the midpoint of line AB cut by ellipse x2 + 4y2 = 36, then the equation of line L is______ ．