The line passing through point P (8,1) intersects hyperbola x2-4y2 = 4 at two points a and B, and P is the midpoint of line ab. the equation of line AB is obtained

The line passing through point P (8,1) intersects hyperbola x2-4y2 = 4 at two points a and B, and P is the midpoint of line ab. the equation of line AB is obtained

Let a (x1, Y1), B (X2, Y2), then X1 + x2 = 16, Y1 + y2 = 2, ∵ x12-4y12 = 4, x22-4y22 = 4, ∵ 16 (x1-x2) - 8 (y1-y2) = 0, ∵ KAB = 2, ∵ the equation of straight line is Y-1 = 2 (X-8), that is, 2x-y-15 = 0

Let a B be a two-point line segment on hyperbola x2-y2 = 1, and the coordinates of the midpoint of AB be (1 / 2,2) to solve the equation of line ab

The midpoint coordinates m (1 / 2,2) of ab
xA+xB=2xM=2*(1/2)=1,yA+yB=2yM=2*2=4
[(xA)^2-(yA)^2]-[(xB)^2-(yB)^2=1-1
(xA+xB)*(xA-xB)-(yA+yB)*(yA-yB)=0
k(AB)=(yA-yB)/(xA-xB)=(xA+xB)/(yA+yB)=1/4
y-2=(1/4)*(x-1/2)
AB:2x-8y+15=0

If a straight line passing through point P (2,2) intersects hyperbola X2 - Y2 / 3 = 1 at two points a and B, and point P is the midpoint of line AB, then the equation of line L

Let the equation of a straight line L passing through M be y = K (X-2) + 2 = kx-2k + 2. (1) the intersection of L and ellipse a (X &;, Y &;), B (X &;, Y &;) m is the midpoint of AB, so: X &; + X &; = 4 y &; + Y &; = 4A, B is in hyperbola X2 - Y2 / 3 = 1, so there is X &;,; + 1