The ellipse 4x & # 178; + Y & # 178; = 1 and the straight line L: y = = x + m are known 1. When a line and an ellipse have a common point, find the value range of the real number M 2. Find the linear equation of the longest chord cut by the ellipse

The ellipse 4x & # 178; + Y & # 178; = 1 and the straight line L: y = = x + m are known 1. When a line and an ellipse have a common point, find the value range of the real number M 2. Find the linear equation of the longest chord cut by the ellipse

4x² + y² = 1
4x² + (x + m)² = 1
5x² + 2mx + (m² - 1) = 0
There is a common point, that is, Δ ≥ 0
(2m)² - 4(5)(m² - 1) ≥ 0
20 - 16m² ≥ 0
- √5/2 ≤ m ≤ √5/2
When the cut chord is the longest, the line passes through the origin
So m = 0
The linear equation is y = X