Through the point m (2,1), make a straight line l-intersection hyperbola x ＾ 2 - (Y ＾ 2) / 2 = 1 at two points a and B, and M is the midpoint of ab. solve the linear l-equation for detailed solution,

Through the point m (2,1), make a straight line l-intersection hyperbola x ＾ 2 - (Y ＾ 2) / 2 = 1 at two points a and B, and M is the midpoint of ab. solve the linear l-equation for detailed solution,

Use the point difference method
The equation is reduced to 2x & # 178; - Y & # 178; = 2
Let a (X &;, Y &;), B (X &;, Y &;), then x &; + X &; = 4, Y &; + Y &; = 2
2x²₁-y²₁=2 (1)
2x²₂-y²₂=2 (2)
(2) - (1) get
2(x²₂- x²₁)-(y²₂- y²₁)=0
2(x₂- x₁)(x₂+ x₁)=(y₂- y₁)(y₂+ y₁)
(y₂- y₁) / (x₂- x₁)= 2(x₁+x₂) / (y₁+y₂)
That is to say, the slope of AB is k = 2 (X &; + X &;) / (Y &; + Y &;) = 4
So the linear equation is Y-1 = 4 (X-2), that is 4x-y-7 = 0