We know the straight line y = x + m and ellipse 4x & # 178; + Y & # 178; = 1 When m is the value, the line and ellipse are separated, tangent and intersect 2 find the linear equation of the longest chord cut by the ellipse

We know the straight line y = x + m and ellipse 4x & # 178; + Y & # 178; = 1 When m is the value, the line and ellipse are separated, tangent and intersect 2 find the linear equation of the longest chord cut by the ellipse

1. The simultaneous two equations eliminate y to get 5x & # 178; + 2mx + M & # 178; - 1 = 0, Δ = (2m) &# 178; - 4 × 5 (M & # 178; - 1) = 5 - 4m & # 178; (1) when Δ √ 5 / 2, they are separated (2) when Δ = 0, i.e. M = ± √ 5 / 2, they are tangent (3) when Δ > 0, i.e. - √ 5 / 2 < m < √ 5 / 2, they intersect 2