Question

椭圆=1的焦点F₁和F₂，P为椭圆上一点，若∠F₁PF₂为锐角，则P点的横坐标的取值范围____________.

Answer 1

答案：(-5,-3)∪(3,5)  设P（x₀,y₀）.

∵F₁(-5,0),F₂(5,0),=(x₀+5,y₀).

=(x₀-5,y₀),·=x₀²-25+y₀²=x₀²-25+20-x₀²＞0,得

x₀＜-3或x₀＞3.

又∵-5＜x₀＜5,∴x₀∈(-5,-3)∪(3,5).